Sensor-based wireless communication systems using compressive sampling

ABSTRACT

Methods, devices and systems for sensor-based wireless communication systems using compressive sampling are provided. In one embodiment, the method for sampling signals comprises receiving, over a wireless channel, a user equipment transmission based on an S-sparse combination of a set of vectors; down converting and discretizing the received transmission to create a discretized signal; correlating the discretized signal with a set of sense waveforms to create a set of samples, wherein a total number of samples in the set is equal to a total number of sense waveforms in the set, wherein the set of sense waveforms does not match the set of vectors, and wherein the total number of sense waveforms in the set of sense waveforms is fewer than a total number of vectors in the set of vectors; and transmitting at least one sample of the set of samples to a remote central processor.

CROSS-REFERENCE TO RELATED APPLICATIONS

This application claims the benefit of U.S. Provisional Application No.U.S. 61/121,992 filed Dec. 12, 2008, entitled “LOW POWER ARCHITECTUREAND REMOTE SAMPLER INVENTIONS.” The foregoing application isincorporated herein by reference in its entirety.

FIELD

This disclosure generally relates to wireless communication systems andmore particularly to methods, devices and systems for using compressivesampling in a sensor-based wireless communication system.

BACKGROUND

Wireless communications systems are widely deployed to provide, forexample, a broad range of voice and data-related services. Typicalwireless communications systems consist of multiple-access communicationnetworks that allow users to share common network resources. Examples ofthese networks are time division multiple access (“TDMA”) systems, codedivision multiple access (“CDMA”) systems, single carrier frequencydivision multiple access (“SC-FDMA”) systems, orthogonal frequencydivision multiple access (“OFDMA”) systems, or other like systems. AnOFDMA system is supported by various technology standards such asevolved universal terrestrial radio access (“E-UTRA”), Wi-Fi, worldwideinteroperability for microwave access (“WiMAX”), ultra mobile broadband(“UMB”), and other similar systems. Further, the implementations ofthese systems are described by specifications developed by variousstandards bodies such as the third generation partnership project(“3GPP”) and 3GPP2.

As wireless communication systems evolve, more advanced networkequipment is introduced that provide improved features, functionalityand performance. Such advanced network equipment may also be referred toas long-term evolution (“LTE”) equipment or long-term evolution advanced(“LTE-A”) equipment. LTE builds on the success of high-speed packetaccess (“HSPA”) with higher average and peak data throughput rates,lower latency and a better user experience, especially in high-demandgeographic areas. LTE accomplishes this higher performance with the useof broader spectrum bandwidth, OFDMA and SC-FDMA air interfaces, andadvanced antenna methods.

Communications between user equipment and base stations may beestablished using single-input, single-output systems (“SISO”), whereonly one antenna is used for both the receiver and transmitter;single-input, multiple-output systems (“SIMO”), where multiple antennasare used at the receiver and only one antenna is used at thetransmitter; and multiple-input, multiple-output systems (“MIMO”), wheremultiple antennas are used at the receiver and transmitter. Compared toa SISO system, SIMO may provide increased coverage while MIMO systemsmay provide increased spectral efficiency and higher data throughput ifthe multiple transmit antennas, multiple receive antennas or both areutilized.

In these wireless communication systems, signal detection and estimationin noise is pervasive. Sampling theorems provide the ability to convertcontinuous-time signals to discrete-time signals to allow for theefficient and effective implementation of signal detection andestimation algorithms. A well-known sampling theorem is often referredto as the Shannon theorem and provides a necessary condition onfrequency bandwidth to allow for an exact recovery of an arbitrarysignal. The necessary condition is that the signal must be sampled at aminimum of twice its maximum frequency, which is also defined as theNyquist rate. Nyquist rate sampling has the drawback of requiringexpensive, high-quality components requiring substantial power and costto support sampling at large frequencies. Further, Nyquist-rate samplingis a function of the maximum frequency of the signal and does notrequire knowledge of any other properties of the signal.

To avoid some of these difficulties, compressive sampling provides a newframework for signal sensing and compression where a special property ofthe input signal, sparseness, is exploited to reduce the number ofvalues needed to reliably represent a signal without loss of desiredinformation.

BRIEF DESCRIPTION OF THE DRAWINGS

To facilitate this disclosure being understood and put into practice bypersons having ordinary skill in the art, reference is now made toexemplary embodiments as illustrated by reference to the accompanyingfigures. Like reference numbers refer to identical or functionallysimilar elements throughout the accompanying figures. The figures alongwith the detailed description are incorporated and form part of thespecification and serve to further illustrate exemplary embodiments andexplain various principles and advantages, in accordance with thisdisclosure, where:

FIG. 1 illustrates one embodiment of a sensor-based wirelesscommunication system using compressive sampling in accordance withvarious aspects set forth herein.

FIG. 2 illustrates another embodiment of a sensor-based wirelesscommunication system using compressive sampling in accordance withvarious aspects set forth herein.

FIG. 3 illustrates another embodiment of a sensor-based wirelesscommunication system using compressive sampling in accordance withvarious aspects set forth herein.

FIG. 4 illustrates one embodiment of a compressive sampling system inaccordance with various aspects set forth herein.

FIG. 5 is a flow chart of one embodiment of a compressive samplingmethod in accordance with various aspects set forth herein.

FIG. 6 illustrates another embodiment of a sensor-based wirelesscommunication system using compressive sampling in accordance withvarious aspects set forth herein.

FIG. 7 illustrates one embodiment of an access method in a sensor-basedwireless communication system using compressive sampling in accordancewith various aspects set forth herein.

FIG. 8 illustrates another embodiment of a sensor-based wirelesscommunication system using compressive sampling in accordance withvarious aspects set forth herein.

FIG. 9 illustrates one embodiment of a quantizing method of a detectorin a sensor-based wireless communication system using compressivesampling in accordance with various aspects set forth herein.

FIG. 10 is a chart illustrating an example of the type of sparserepresentation matrix and sensing matrix used in a sensor-based wirelesscommunication system using compressive sampling in accordance withvarious aspects set forth herein.

FIG. 11 illustrates one embodiment of a wireless device, which can beused in a sensor-based wireless communication system using compressivesampling in accordance with various aspects set forth herein.

FIG. 12 illustrates one embodiment of a sensor, which can be used in asensor-based wireless communication system using compressive sampling inaccordance with various aspects set forth herein.

FIG. 13 illustrates one embodiment of a base station, which can be usedin a sensor-based wireless communication system using compressivesampling in accordance with various aspects set forth herein.

FIG. 14 illustrates simulated results of one embodiment of detecting awireless device in a sensor-based wireless communication system usingcompressive sampling in accordance with various aspects set forthherein.

FIG. 15 illustrates simulated results of the performance of oneembodiment of a sensor-based wireless communication system usingcompressive sampling in accordance with various aspects set forthherein.

FIG. 16 illustrates simulated results of the performance of oneembodiment of a sensor-based wireless communication system usingcompressive sampling in accordance with various aspects set forthherein.

FIG. 17 illustrates simulated results of the performance of oneembodiment of a sensor-based wireless communication system usingcompressive sampling in accordance with various aspects set forthherein.

FIG. 18 illustrates simulated results of the performance of oneembodiment of a sensor-based wireless communication system usingcompressive sampling in accordance with various aspects set forthherein.

FIG. 19 illustrates simulated results of the performance of oneembodiment of a sensor-based wireless communication system usingcompressive sampling in accordance with various aspects set forthherein.

FIG. 20 is an example of deterministic matrices used in one embodimentof a sensor-based wireless communication system using compressivesampling in accordance with various aspects set forth herein.

FIG. 21 is an example of random matrices used in one embodiment of asensor-based wireless communication system using compressive sampling inaccordance with various aspects set forth herein.

FIG. 22 illustrates an example of an incoherent sampling system in anoise-free environment.

FIG. 23 illustrates another embodiment of a sensor-based wirelesscommunication system using compressive sampling in accordance withvarious aspects set forth herein.

FIG. 24 illustrates an example of a prior art lossless sampling system.

FIG. 25 illustrates another embodiment of a sensor-based wirelesscommunication system using compressive sampling in a noisy environmentin accordance with various aspects set forth herein.

FIG. 26 illustrates another embodiment of an access method in asensor-based wireless communication system using compressive sampling inaccordance with various aspects set forth herein.

FIG. 27 illustrates another embodiment of a sensor-based wirelesscommunication system using compressive sampling in a noisy environmentin accordance with various aspects set forth herein.

FIG. 28 illustrates another embodiment of a sensor-based wirelesscommunication system using compressive sampling in accordance withvarious aspects set forth herein.

FIG. 29 illustrates another embodiment of a sensor-based wirelesscommunication system using compressive sampling in accordance withvarious aspects set forth herein.

Skilled artisans will appreciate that elements in the accompanyingfigures are illustrated for clarity, simplicity and to further helpimprove understanding of the embodiments, and have not necessarily beendrawn to scale.

DETAILED DESCRIPTION

Although the following discloses exemplary methods, devices and systemsfor use in sensor-based wireless communication systems, it will beunderstood by one of ordinary skill in the art that the teachings ofthis disclosure are in no way limited to the examplaries shown. On thecontrary, it is contemplated that the teachings of this disclosure maybe implemented in alternative configurations and environments. Forexample, although the exemplary methods, devices and systems describedherein are described in conjunction with a configuration foraforementioned sensor-based wireless communication systems, the skilledartisan will readily recognize that the exemplary methods, devices andsystems may be used in other systems and may be configured to correspondto such other systems as needed. Accordingly, while the followingdescribes exemplary methods, devices and systems of use thereof, personsof ordinary skill in the art will appreciate that the disclosedexamplaries are not the only way to implement such methods, devices andsystems, and the drawings and descriptions should be regarded asillustrative in nature and not restrictive.

Various techniques described herein can be used for various sensor-basedwireless communication systems. The various aspects described herein arepresented as methods, devices and systems that can include a number ofcomponents, elements, members, modules, nodes, peripherals, or the like.Further, these methods, devices and systems can include or not includeadditional components, elements, members, modules, nodes, peripherals,or the like. In addition, various aspects described herein can beimplemented in hardware, firmware, software or any combination thereof.It is important to note that the terms “network” and “system” can beused interchangeably. Relational terms described herein such as “above”and “below”, “left” and “right”, “first” and “second”, and the like maybe used solely to distinguish one entity or action from another entityor action without necessarily requiring or implying any actual suchrelationship or order between such entities or actions. The term “or” isintended to mean an inclusive “or” rather than an exclusive “or.”Further, the terms “a” and “an” are intended to mean one or more unlessspecified otherwise or clear from the context to be directed to asingular form.

The wireless communication system may be comprised of a plurality ofuser equipment and an infrastructure. The infrastructure includes thepart of the wireless communication system that is not the userequipment, such as sensors, base stations, core network, downlinktransmitter, other elements and combination of elements. The corenetwork can have access to other networks. The core network, alsoreferred to as a central brain or remote central processor, may includea high-powered infrastructure component, which can performcomputationally intensive functions at a high rate with acceptablefinancial cost. The core network may include infrastructure elements,which can communicate with base stations so that, for instance, physicallayer functions may also be performed by the core network. The basestation may communicate control information to a downlink transmitter toovercome, for instance, communication impairments associated withchannel fading. Channel fading includes how a radio frequency (“RF”)signal can be bounced off many reflectors and the properties of theresulting sum of reflections. The core network and the base station may,for instance, be the same the same infrastructure element, share aportion of the same infrastructure element or be differentinfrastructure elements.

A base station may be referred to as a node-B (“NodeB”), a basetransceiver station (“BTS”), an access point (“AP”), a satellite, arouter, or some other equivalent terminology. A base station may containa RF transmitter, RF receiver or both coupled to a antenna to allow forcommunication with a user equipment.

A sensor may be referred to as a remote sampler, remote conversiondevice, remote sensor or other similar terms. A sensor may include, forinstance, an antenna, a receiving element, a sampler, a controller, amemory and a transmitter. A sensor may be interfaced to, for instance, abase station. Further, sensors may be deployed in a wirelesscommunication system that includes a core network, which may have accessto another network.

A user equipment used in a wireless communication system may be referredto as a mobile station (“MS”), a terminal, a cellular phone, a cellularhandset, a personal digital assistant (“PDA”), a smartphone, a handheldcomputer, a desktop computer, a laptop computer, a tablet computer, anetbook, a printer, a set-top box, a television, a wireless appliance,or some other equivalent terminology. A user equipment may contain an RFtransmitter, RF receiver or both coupled to an antenna to communicatewith a base station. Further, a user equipment may be fixed or mobileand may have the ability to move through a wireless communicationsystem. Further, uplink communication refers to communication from auser equipment to a base station, sensor or both. Downlink communicationrefers to communication from a base station, downlink transmitter orboth to a user equipment.

FIG. 1 illustrates one embodiment of sensor-based wireless communicationsystem 100 using compressive sampling with various aspects describedherein. In this embodiment, system 100 can provide robust, highbandwidth, real-time wireless communication with support for high-userdensity. System 100 can include user equipment 106, sensors 110 to 113,base station 102, core network 103 and other network 104. User equipment106 may be, for instance, a low cost, low power device. Base station 102can communicate with user equipment 106 using, for instance, a pluralityof low-cost, low-power sensors 110 to 113.

In FIG. 1, system 100 contains sensors 110 to 113 coupled to basestation 102 for receiving communication from user equipment 106. Basestation 102 can be coupled to core network 103, which may have access toother network 104. In one embodiment, sensors 110 to 113 may beseparated by, for instance, approximately ten meters to a few hundredmeters. In another embodiment, a single sensor 110 to 113 may be used. Aperson of ordinary skill in the art will appreciate in deploying asensor-based wireless communication system that there are tradeoffsbetween the power consumption of sensors, deployment cost, systemcapacity, other factors and combination factors. For instance, assensors 110 to 113 become more proximally spaced, the power consumptionof sensors 110 to 113 may decrease while the deployment cost and systemcapacity may increase. Further, user equipment 106 may operate using adifferent RF band than used with the underlying wireless network when inclose proximity to sensors 110 to 113.

In the current embodiment, sensors 110 to 113 can be coupled to basestation 102 using communication links 114 to 117, respectively, whichcan support, for instance, a fiber-optic cable connection, a coaxialcable connection, other connections or any combination thereof. Further,a plurality of base stations 102 may communicate sensor-basedinformation between each other to support various functions. Sensors 110to 113 may be designed to be low cost with, for example, an antenna, anRF front-end, baseband circuitry, interface circuitry, a controller,memory, other elements, or combination of elements. A plurality ofsensors 110 to 113 may be used to support, for instance, antenna arrayoperation, SIMO operation, MIMO operation, beamforming operation, otheroperations or combination of operations. A person of ordinary skill inthe art will recognize that the aforementioned operations may allow userequipment 106 to transmit at a lower power level resulting in, forinstance, lower power consumption.

In system 100, user equipment 106 and base station 102 can communicateusing, for instance, a network protocol. The network protocol can be,for example, a cellular network protocol, Bluetooth protocol, wirelesslocal area loop (“WLAN”) protocol or any other protocol or combinationof protocols. A person of ordinary skill in the art will recognize thata cellular network protocol can be anyone of many standardized cellularnetwork protocols used in systems such as LTE, UMTS, CDMA, GSM andothers. The portion of the network protocol executed by sensors 110 to113 may include, for instance, a portion of the physical layerfunctions. A person of ordinary skill in the art will recognize thatreduced functionality performed by sensors 110 to 113 may result inlower cost, smaller size, reduced power consumption, other advantages orcombination of advantages.

Sensors 110 to 113 can be powered by, for instance, a battery powersource, an alternating current (“AC”) electric power source or otherpower sources or combination of power sources. Communication includingreal-time communication among sensors 110 to 113, user equipment 106,base station 102, core network 103, other network 104 or any combinationthereof may be supported using, for instance, an automatic repeatrequest (“ARQ”) protocol.

In the current embodiment, sensors 110 to 113 can compress a receiveduplink signal (“f”) transmitted from user equipment 106 to form a sensedsignal (“y”). Sensors 110 to 113 can provide the sensed signal (“y”) tobase station 102 using communication links 114 to 117, respectively.Base station 102 can then process the sensed signal (“y”). Base station102 may communicate instructions to sensors 110 to 113, wherein theinstructions can relate to, for instance, data conversion, oscillatortuning, beam steering using phase sampling, other instructions orcombination of instructions. Further, user equipment 106, sensors 110 to113, base station 102, core network 103, other network 104 or anycombination thereof may communicate including real-time communicationusing, for instance, a medium access control (“MAC”) hybrid-ARQprotocol, other similar protocols or combination of protocols. Also,user equipment 106, sensors 110 to 113, base station 102, core network103, other network 104 or any combination thereof may communicate using,for instance, presence signaling codes which may operate without theneed for cooperation from sensors 110 to 113; space-time codes which mayrequire channel knowledge; fountain codes which may be used forregistration and real-time transmission; other communication codes orcombination of communication codes. Some of these communication codesmay require, for instance, applying various signal processing techniquesto take advantage of any inherent properties of the codes.

In FIG. 1, base station 102 may perform functions such as transmittingsystem overhead information; detecting the presence of user equipment106 using sensors 110 to 113; two-way, real-time communication with userequipment 106; other functions or combination of functions. A person ofordinary skill in the art will recognize that sensors 110 to 113 may besubstantially less expensive than base station 102 and core network 103.

Sampling is performed by measuring the value of a continuous-time signalat a periodic rate, aperiodic rate, or both to form a discrete-timesignal. In the current embodiment, the effective sampling rate ofsensors 110 to 113 can be less than the actual sampling rate used bysensors 110 to 113. The actual sampling rate is the sampling rate of,for instance, an analog-to-digital converter (“ADC”). The effectivesampling rate is measured at the output of sensors 110 to 113, whichcorresponds to the bandwidth of sensed signal (“y”). By providing alower effective sampling rate, sensors 110 to 113 can consume less powerthan other sensors operating at the actual sampling rate without anycompression. Redundancy can be designed into the deployment of a systemso that the loss of a sensor would minimally affect the performance ofthe system. For many types of signals, reconstruction of such signalscan be performed by base station 102, core network 103, other network104, or any combination thereof.

In the current embodiment, sensors 110 to 113 may each contain a directsequence de-spreading element, a fast Fourier transform (“FFT”) element,other elements or combination of elements. Base station 102 can send tosensor 110 to 113 instructions, for instance, to select direct sequencecodes or sub-chip timing for a de-spreading element, to select thenumber of frequency bins or the spectral band for an FFT element, otherinstructions or combination of instructions. These instructions may becommunicated at, for example, one-millisecond intervals, with eachinstruction being performed by sensor 110 to 113 within one tenth of amillisecond after being received. Further, user equipment 106 maytransmit and receive information in the form of slots, packets, framesor other similar structures, which may have a duration of, for instance,one to five milliseconds. Slots, packets, frames and other similarstructures may include a collection of time-domain samples successivelycaptured or may describe a collection of successive real or complexvalues.

In FIG. 100, system 100 can include the communication of system overheadinformation between user equipment 106, base station 102, core network103, other network 104, sensors 110 to 113 or any combination thereof.The system overhead information may include, for instance, guiding andsynchronizing information, wireless wide area network information, WLANinformation, other information or combination of information. A personof ordinary skill in the art will recognize that by limiting the needfor user equipment 106 to monitor the underlying network, extraneousnetworks or both may reduce its power consumption.

In FIG. 1, user equipment 106 may transmit uplink signals at a lowtransmission power level if user equipment 106 is sufficiently proximateto sensors 110 to 113. Sensors 110 to 113 can compressively sample thereceived uplink signals (“g”) to generate sensed signals (“y”). Sensors110 to 113 can send sensed signals (“y”) to base station 102 usingcommunication link 114 to 117, respectively. Base station 102 mayperform, for instance, layer 1 functions such as demodulation anddecoding; layer 2 functions such as packet numbering and ARQ; andhigher-layer functions such as registration, channel assignment andhandoff. Base station 102 may have substantial computational power toperform computationally intensive functions in real time, near-real timeor both.

In the current embodiment, base station 102 may apply link adaptationstrategies using, for instance, knowledge of the communication channelssuch as the antenna correlation matrix of user equipment 106; the numberof sensors 110 to 113 in proximity to user equipment 106; other factorsor combination of factors. Such adaptation strategies may requireprocessing at periodic intervals, for instance, one-millisecondintervals. Such strategies may allow for operating, for instance, at theoptimum space-time multiplexing gain and diversity gain. Also, aplurality of base stations 102 may communicate between each other toperform, for instance, dirty paper coding (“DPC”), which is a techniquefor efficiently transmitting downlink signals through a communicationchannel that is subject to some interference that is known to basestation 102. To support these techniques, other base stations thatreceive extraneous uplink signals from user equipment 106 may providethe uplink signals (“f”) to base station 102 associated with userequipment 106. A person of ordinary skill in the art will recognize thata plurality of user equipment 106 can communicate with base station 102.

FIG. 2 illustrates another embodiment of a sensor-based wirelesscommunication system 200 using compressive sampling in accordance withvarious aspects set forth herein. In this embodiment, system 200 canprovide robust, high bandwidth, real-time wireless communication withsupport for high-user density. System 200 includes user equipment 206,sensors 210 to 213, base station 202, core network 203 and other network204. In this embodiment, sensors 210 to 213 may perform a portion oflayer 1 functions such as receiving an uplink signal and performingcompressive sampling. Further, base station 202 may send instructions tosensors 210 to 213 using communication link 214 to 217, respectively.Such instructions may be, for example, to compress using a specificmultiple access code such as a direct sequence code or an OFDM code.Further, base station 202 may send instructions to sensors 210 to 213 toperform, for instance, sampling at twice the sampling rate, which may beat a specific phase.

Base station 202 may perform computationally intensive functions to, forinstance, detect the presence of user equipment 206 in the sensedsignals (“y”) received from sensors 210 to 213. Once the presence ofuser equipment 206 is detected, base station 202 may configure sensors210 to 213 to improve the reception of uplink signals (“f”) from userequipment 206. Such improvements may be associated with timing,frequency, coding, other characteristics or combination ofcharacteristics. Further, user equipment 206 may transmit uplink signals(“f”) using, for instance, a fountain code. For high bandwidth, lowpower communication, user equipment 206 may use a fountain code totransmit uplink signals containing, for instance, real-time speech. Thepacket transmission rate for such uplink signals may be, for instance,in the range of 200 Hz to 1 kHz. Sensors 210 to 213 may have limiteddecision-making capability with substantial control by base station 202.

In FIG. 2, sensors 210 to 213 may be densely deployed, for instance, onesensor 210 to 213 in approximately every one hundred meters separationdistance, one sensor 210 to 213 in approximately every ten metersseparation distance, other configurations or combination ofconfigurations. Sensors 210 to 213 may contain or be co-located with adownlink transmitter, which is used to support the transmission ofdownlink signals received from base station 202. Further, base station202 may use a communication link to provide downlink signals to a remotedownlink transmitter such as, a traditional cellular tower with antennasectorization, a cellular transmitter mounted on a building or lightpole, a low power unit in an office, other elements or combination ofelements. The deployment of such remote downlink transmitters may be tosupport, for example, building deployment, street light deployment,other deployments or combination of deployments. Further, it will beunderstood that a plurality of user equipment 206 can communicate withbase station 202.

FIG. 3 illustrates another embodiment of a sensor-based wirelesscommunication system 300 using compressive sampling in accordance withvarious aspects set forth herein. In this embodiment, system 300represents a multiple access system. System 300 includes user equipment306, sensor 310, base station 302 and downlink transmitter 308. In FIG.3, sensor 310 can include a receiving element for downconverting uplinksignals. A person of ordinary skill in the art will appreciate thedesign and implementation requirements for such a receiving element.

In FIG. 3, base station 302 can be coupled to downlink transmitter 308,wherein downlink transmitter 308 can be co-located, for instance, with acellular tower. Base station 302 may contain, for instance, a collectorfor collecting sensed signals from sensor 310, a detector for detectinginformation signals contained in the sensed signals, a controller forcontrolling sensor 310, other elements or combination of elements. Basestation 302 and downlink transmitter 308 may be co-located. Further,downlink transmitter 308 can be coupled to base station 302 usingcommunication link 309, which can support, for instance, a fiber-opticcable connection, a microwave link, a coaxial cable connection, otherconnections or any combination thereof. The configuration of system 300may be similar to a conventional cellular system such as, a GSM system,a UMTS system, a LTE system, a CDMA system, other systems or combinationof systems. A person of ordinary skill in the art will recognize thatthese systems exhibit arrangements of user equipment, base stations,downlink transmitters, other elements or combination of elements.

In the current embodiment, user equipment 308 and base station 302 cancommunicate using a network protocol to perform functions such as randomaccess; paging; origination; resource allocation; channel assignment;overhead signaling including timing, pilot system identification,channels allowed for access; handover messaging; training or pilotsignaling; other functions or combination of functions. Further, userequipment 308 and base station 302 may communicate voice information,packet data information, circuit-switched data information, otherinformation or combination of information.

FIG. 4 illustrates one embodiment of a compressive sampling system inaccordance with various aspects set forth herein. System 400 includescompressive sampler 431 and detector 452. In FIG. 4, compressive sampler431 can compressively sample an input signal (“f”) using sensingwaveforms (“φ_(j)”) of sensing matrix (“Φ”) to generate a sensed signal(“y”), where φ_(j) refers to the jth waveform of sensing matrix (“Φ”).The input signal (“f”) can be of length N, the sensing matrix (“Φ”) canhave M sensing waveforms (“φ_(j)”) of length N and the sensed signal(“y”) can be of length M, where M can be less than N. An informationsignal (“x”) can be recovered if the input signal (“f”) is sufficientlysparse. A person of ordinary skill in the art will recognize thecharacteristics of a sparse signal. In one definition, a signal oflength N with S non-zero values is referred to as S-sparse and includesN minus S (“N−S”) zero values.

In the current embodiment, compressive sampler 431 can compressivelysample the input signal (“f”) using, for instance, Equation (1).

y_(k)=

f,φ_(k)

,kεJ such that J⊂{1, . . . , N},  (1)

where the brackets

denote the inner product, correlation function or other similarfunctions.

Further, detector 452 can solve the sensed signal (“y”) to find theinformation signal (“x”) using, for instance, Equation (2).

min_({tilde over (x)}ε)

_(N) ∥{tilde over (x)}∥

₁ subject to y _(k)=

φ_(k) ,Ψ{tilde over (x)}

,∀kεJ,  (2)

where ∥ ∥

₁ is the

₁ norm, which is the sum of the absolute values of the elements of itsargument and the brackets

denote the inner product, correlation function or other similarfunctions. One method, for instance, which can be applied for

₁ minimization is the simplex method. Other methods to solve the sensedsignal (“y”) to find the information signal (“x”) include using, forinstance, the

₀ norm algorithm, other methods or combination of methods.

Incoherent sampling is a form of compressive sampling that relies onsensing waveforms (“φ_(j)”) of the sensing matrix (“Φ”) beingsufficiently unrelated to the sparse representation matrix (“Ψ”), whichis used to make the input signal (“f”) sparse. To minimize the requirednumber of sensing waveforms (“φ_(j)”) of sensing matrix (“Φ”), thecoherence (“μ”) between the sparse representation waveforms (“ψ_(j)”) ofthe sparse representation matrix (“Ψ”) and the sensing waveforms(“φ_(j)”) of sensing matrix (“Φ”) should represent that these waveformsare sufficiently unrelated, corresponding to a lower coherence (“μ”),where ψ_(j) refers to the jth waveform of the sparse representationmatrix (“Ψ”). The coherence (“μ”) can be represented, for instance, byEquation 3.

μ(Φ,Ψ)=√{square root over (N)}max_(1≦k,j≦N)∥

φ_(k),ψ_(j)

∥

₁ ,  (3)

where ∥ ∥

₁ is the

₁ norm, which is the sum of the absolute values of the elements of itsargument and the brackets

denote the inner product, correlation function or other similarfunctions.

FIG. 5 is a flow chart of an embodiment of a compressive sampling method500 in accordance with various aspects set forth herein, which can beused, for instance, to design a compressive sampling system. In FIG. 5,method 500 can start at block 570, where method 500 can model an inputsignal (“f”) and discover a sparse representation matrix (“Ψ”) in whichthe input signal (“f”) is S-sparse. At block 571, method 500 can choosea sensing matrix (“Φ”), which is sufficiently incoherent with the sparserepresentation matrix (“Ψ”). At block 572, method 500 can randomly,deterministically or both select M sensing waveforms (“φ_(j)”) ofsensing matrix (“Φ”), where M may be greater than or equal to S. Atblock 573, method 500 can sample input signal (“f”) using the selected Msensing waveforms (“φ_(j)”) to produce a sensed signal (“y”). At block574, method 500 can pass the sparse representation matrix (“Ψ”), thesensing matrix (“Φ”) and the sensed signal (“y”) to a detector torecover an information signal (“x”).

FIG. 6 illustrates another embodiment of a sensor-based wirelesscommunication system using compressive sampling in accordance withvarious aspects set forth herein. In this embodiment, system 600 canprovide robust, high bandwidth, real-time wireless communication withsupport for high-user density. System 600 includes user equipment 606,sensor 610 and base station 602. In FIG. 6, system 600 can allow userequipment 606 to communicate with, for instance, the underlying cellularsystem even if sensor 610, for instance, fails to operate. System 600may allow sensors 610 to be widely distributed consistent with, forinstance, office-building environments. System 600 may allow for basestation 602 to not be limited by, for instance, computational capacity,memory, other resources or combination of resources. System 600 mayallow for downlink signals to be provided by, for instance, aconventional cellular tower. System 600 may allow user equipment 606 tominimize power consumption by limiting its transmission power level to,for instance, approximately ten to one hundred microwatts. System 600may allow for sensor 610 to be coupled to base station 602 usingcommunication link 614, wherein communication link 614 can support, forinstance, a fiber-optic cable connection, a coaxial cable connection,other connections or any combination thereof. System 600 may allow forsensor 610 to be operated by power sources such as a battery, aphotovoltaic power source, an alternating current (“AC”) electric powersource, other power sources or combination of power sources.

In FIG. 6, system 600 may allow for sensor 610 to be substantially lessex pensive than base station 602. Further, system 600 may allow forsensor 610 to operate using battery power for an extended period such asapproximately one to two years. To achieve this, a person of ordinaryskill in the art will recognize that certain functions such as signaldetection, demodulation and decoding may have to be performed by, forinstance, base station 602.

In FIG. 6, sensor 610 can have a receiving element such as an antennacoupled to an RF downconversion chain, which are used for receivinguplink signals (“f”). In this disclosure, uplink signal (“f”) can alsobe referred to as uplink signal (“g”). Uplink signal (“g”) includeschannel propagation effects and environmental effects on uplink signal(“f”). For instance, channel gain (“a”) 621 of channel 620 canrepresent, for instance, channel propagation effects while channel noise(“v”) 622 of channel 620 can represent, for instance, environment noiseeffects. Further, sensor 610 can support a communication link to send,for instance, sensed signals (“y”) to base station 602. Sensor 610 maynot have the computational capability to, for instance, recognize whenuser equipment 606 is transmitting an uplink signal (“f”). Sensor 610may receive instructions from base station 602 associated with, forinstance, RF downconversion, compressive sampling, other functions orcombination of functions.

There are many methods for a user equipment to access a wirelesscommunication system. One type of access method is, for instance, theAloha random access method, which is performed when an unrecognized userequipment attempts to access the network. Two-way communication with abase station may take place, for instance, after the user equipment hasbeen given permission to use the system and any uplink and downlinkchannels have been assigned.

FIG. 7 illustrates one embodiment of an access method 700 in asensor-based wireless communication system using compressive sampling inaccordance with various aspects set forth herein. Various illustrativestructures are shown in the lower portion of FIG. 7 to facilitateunderstanding of method 700. Further, FIG. 7 illustrates base station702 twice but should be interpreted as one and the same base station702. Accordingly, method 700 includes communication amongst base station702, user equipment 706, sensor 710 or any combination thereof. Userequipment 706 can have, for instance, a power-on event 770 and beginobserving overhead messages 771 sent from base station 702. A person ofordinary skill in the art will recognize that a base station cancommunicate with a user equipment using, for instance, broadcastcommunication, point-to-multipoint communication, point-to-pointcommunication or other communication methods or combination ofcommunication methods. Overhead messages 771 may contain systemparameters including, for instance, the length of message frames, thevalue of M associated with the number of sensing waveforms (“φ_(j)”) andthe sparseness S of the uplink signals (“f”) being sent.

In FIG. 7, base station 702 may send, for instance, an overhead messageto configure user equipment 706 to use sparseness S₁ and sparserepresentation matrix (“Ψ”), as shown at 772. User equipment 706 maythen send, for instance, presence signals using sparseness S₁, asrepresented by 780. Presence signals can include any signal sent by userequipment 706 to base station 702 that can be compressively sampled. Inanother embodiment, user equipment 706 may send presence signals usingS₁, as shown at 780, when it determines that it is approaching basestation 702. In this situation, user equipment 706 may determine that itis approaching base station 702 via, for instance, overhead messages 771sent by base station 702, another base station or both.

In FIG. 7, base station 702 may also send, for instance, an overheadmessage containing system information such as framing, timing, systemidentification, other system information or combination of information,as shown at 773. In addition, base station 702 may instruct sensor 710to use, for instance, M₁ sensing waveforms (“φ_(j)”) of sensing matrix(“Φ”), as represented by 791. Sensor 710 may then continuously processreceived uplink signals (“f”) and send sensed signals (“y”) using M₁sensing waveforms (“φ_(j)”) of sensing matrix (“Φ”) to base station 702,as shown at 790.

In FIG. 7, base station 702 may send, for instance, an overhead messageto configure user equipment 706 to use sparseness S₂ and sparserepresentation matrix (“Ψ”), as represented by 774. User equipment 706may then send, for instance, presence signals using sparseness S₂, asshown by 781. In addition, base station 702 may instruct sensor 710 touse, for instance, M₂ sensing waveforms (“φ_(j)”) of sensing matrix(“Φ”), as represented by 792. Sensor 710 may then continuously processreceived uplink signals (“f”) and send to base station 702 sensedsignals (“y”) using M₂ sensing waveforms (“φ_(j)”) of sensing matrix(“Φ”), as shown at 793. User equipment 706 may continue to send presencesignals using S₂, as shown by 781, until, for instance, base station 702detects the presence signals using S₂, as shown at 794. At which point,base station 702 may send to user equipment 706 a recognition messageincluding, for instance, a request to send a portion of its electronicserial number (“ESN”) and to use sparseness S₃ and a sparserepresentation matrix (“Ψ”), as represented by 775. Further, basestation 702 may send to sensor 710 an instruction to use, for instance,a new value of M₃ and a new sensing matrix (“Φ”), as shown at 795.Sensor 710 may then continuously process received uplink signals (“f”)and send to base station 702 sensed signals (“y”) using M₃ sensingwaveforms (“φ_(j)”) of sensing matrix (“Φ”), as shown at 796.

In FIG. 7, user equipment 706 may send to base station 702 an uplinkmessage containing a portion of its ESN using S₃, as represented by 782.Once base station 702 has received this uplink message, base station 702may send to user equipment 706 a downlink message requesting userequipment 706 to send, for instance, its full ESN and a request forresources, as shown at 776. User equipment 706 may then send an uplinkmessage containing its full ESN and a request for resources using S₃, asrepresented by 783. After base station 702 receives this uplink message,base station 702 may verify the full ESN of user equipment 706 todetermine its eligibility to be on the system and to assign it anyresources, as represented by 798. Base station 702 may then send to userequipment 706 a downlink message to assign it resources, as shown at777.

Sensor 710 may continuously receive uplink signals (“f”) of a frequencybandwidth (“B”) centered at a center frequency (“f_(c)”). Sensor 710 candownconvert the uplink signal (“f”) using a receiving element and thenperform compressive sampling. Compressive sampling is performed, forinstance, by sampling the received uplink signal (“f”) and thencomputing the product of a sensing matrix (“Φ”) and the samples togenerate a sensed signal (“y”). Sampling may be performed, for instance,at the frequency bandwidth (“B”) corresponding to the Nyquist rate,consistent with preserving the received uplink signal (“f”) according toShannon's theorem. The received uplink signal (“f”) can be sampled, forinstance, periodically, aperiodically or both.

The sampling process can result in N samples, while computing theproduct of a sensing matrix (“Φ”) and the N samples can result in Mvalues of sensed signal (“y”). The sensing matrix (“Φ”) may havedimensions of N by M. These resulting M values of sensed signal (“y”)can be sent over a communication link to base station 702. Compressivesampling can reduce the number of samples sent to base station 702 fromN samples for a conventional approach to M samples, wherein M can beless than N. If sensor 710 does not have sufficient system timing,sampling may be performed at a higher sampling rate resulting in, forinstance, 2N samples. For this scenario, sensor 710 may compute theproduct of a sensing matrix (“Φ”) and the 2N samples of uplink signal(“f”) resulting in 2M samples of sensed signal (“y”). Thus, thecompressive sampler may reduce the number of samples sent to basestation 702 from 2N samples for a conventional approach to 2M samples,wherein M may be less than N. For this scenario, the sensing matrix(“Φ”) may have dimensions of 2N by 2M.

The compressive sampler may compute sensed signal (“y”) by correlatingthe sampled received uplink signal (“f”) with, for instance,independently selected sensing waveforms (“φ_(j)”) of the sensing matrix(“Φ”). Selection of the sensing waveforms (“φ_(j)”) of the sensingmatrix (“Φ”) may be without any knowledge of the information signal(“x”). However, the selection of M may rely, for instance, on anestimate of the sparseness S of the received uplink signal (“f”).Therefore, the selected M sensing waveforms (“φ_(j)”) of the sensingmatrix (“Φ”) may be independent of the sparse representation matrix(“Ψ”), but M may be dependent on an estimate of a property of thereceived uplink signal (“f”). Further, the sparseness S of receiveduplink signal (“f”) may be controlled, for instance, by base station 702sending to user equipment 706 a downlink message recognizing userequipment 706 and configuring user equipment 706 to use sparseness S₃and a new sparse representation matrix (“Ψ”) 775.

Successful detection of the information signal (“x”) by base station 702may require M to be greater than or equal to the sparseness S. The lackof knowledge of sparseness S may be overcome, for instance, by basestation 702 estimating sparseness S and adjusting thereafter. Forexample, base station 702 may initialize M to, for instance, the valueof N, which may correspond to no compression benefit As base station 702estimates the activity level of the frequency band B received at sensor710, base station 702 may, for instance, adjust the value of M. By doingso, base station 702 can affect the power consumption of sensor 710 by,for instance, adjusting the number of M sensing waveforms (“φ_(j)”);thus, adjusting the bandwidth of the sensed signals (“y”) sent to basestation 702 over the communication link.

Further, base station 702 may send an instruction to sensor 710 to, forinstance, periodically increase the value of M to allow base station 702to evaluate thoroughly the sparseness S in the frequency band B. Inaddition, base station 702 may send to sensor 710 an instruction as tothe method of selecting sensing waveforms (“φ_(j)”) such as, randomselection, selection according to a schedule, other selection methods orcombination of selection methods. In some instances, sensor 710 may needto communicate its selection of sensing waveforms (“φ_(j)”) to basestation 702.

User equipment 706 can send presence signals to notify base station 702of its presence. Each presence signal may be an informative signalgenerated by, for instance, selecting and combining sparserepresentation waveforms (“ψ_(j)”) of sparse representation matrix(“Ψ”). The selection of sparse representation waveforms (“ψ_(j)”) ofsparse representation matrix (“Ψ”) may be configured, for instance, byan overhead message sent by base station 702. For example, base station702 may broadcast an overhead message that specifies a subset of sparserepresentation waveforms (“ψ_(j)”) of sparse representation matrix(“Ψ”).

Base station 702 may also broadcast a downlink overhead message forunrecognized user equipment 706 to use a specific sparse representationwaveform (“ψ_(j)”) of sparse representation matrix (“Ψ”), which can bereferred to as a pilot signal (“ψ₀”). Sensor 710 can continuouslyreceive uplink signals (“f”), compressively sample uplink signals (“f”)to generate sensed signal (“y”), and send sensed signals (“y”) to basestation 702. Base station 702 can then detect the pilot signal (“ψ₀”) inthe sensed signal (“y”). Once the pilot signal (“ψ₀”) is detected, basestation 702 may estimate the channel gain (“â”) between user equipment706 and sensor 710 and may instruct any user equipment 706, which hadsent the pilot signal (“ψ₀”), to send, for instance, a portion of itsESN. If a collision occurs between uplink transmissions from differentuser equipment 706, collision resolution methods such as the Alohaalgorithm may be used to separate subsequent uplink transmissionattempts by different user equipment 706.

Sensor 710 may also operate irrespective of the communication betweenbase station 702 and user equipment 706. Base station 702 may instructsensor 710 to use, for instance, M sparse representation waveform(“ψ_(j)”) of sparse representation matrix (“Ψ”). Further, base station702 may vary the value of M based on anticipating, for instance, theamount of uplink signal (“f”) activity by user equipment 706. Forexample, if base station 702 anticipates that the sparseness S of uplinksignal (“f”) is changing, it may instruct sensor 710 to change the valueof M. For a certain deterministic sensing matrix (“Φ”), when M equalsthe value of N, sensing matrix (“Φ”) in sensor 710 may effectivelybecome a discrete Fourier transform (“DFT”).

FIG. 8 illustrates another embodiment of a sensor-based wirelesscommunication system 800 using compressive sampling in accordance withvarious aspects set forth herein. In this embodiment, system 800 canprovide robust, high bandwidth, real-time wireless communication withsupport for high-user density. In FIG. 8, system 800 includes userequipment 806, sensor 810 and base station 802. Base station 802 canreceive sensed signals (“y”) from sensor 810 as input to detector 851 ofbase station 802 to generate an estimate of information signal (“x”),also referred to as {tilde over (x)}. Base station 802 can then quantizethis estimate to generate, for instance, a quantized estimate of theinformation signal (“x”), also referred to as {circumflex over (x)}. Theestimate of the information signal (“x”) may be determined using, forinstance, the simplex algorithm,

₁ norm algorithm,

₀ norm algorithm, other algorithms or combination of algorithms. In thisembodiment, all of the elements of the estimate of the informationsignal (“x”) may have non-zero values. Therefore, a hard decision of theestimate of the information signal (“x”) may be performed to determinethe information signal (“x”), which consists of, for instance, Snon-zero values and N minus S (“N−S”) zero values.

FIG. 9 illustrates one embodiment of a quantizing method 900 of adetector in a sensor-based wireless communication system usingcompressive sampling in accordance with various aspects set forthherein. FIG. 9 refers to steps within base station 902 and steps withinquantizer 953 within base station 902. Method 900 starts at sensor 910,which can send sensed signal (“y”) to base station 902. At block 952,method 900 can solve sensed signal (“y”) to determine an estimate of theinformation signal (“x”), also referred to as {tilde over (x)}. At block970, method 900 can order the elements of the estimate of theinformation signal (“x”), for instance, from the largest value to thesmallest value.

In FIG. 9, the information signal (“x”) is applied to quantizer 953. Atblock 971, method 900 can determine the sparseness S using, forinstance, the sensed signal (“y”), the estimate of the informationsignal (“x”) or both. Further, base station 902 may fix the value of Sfor a user equipment, by sending a downlink message to the userequipment. Base station 902 may also periodically scan for appropriatevalues of S by sending different values of S to the sensor anddetermining the sparseness S of uplink signal (“f”) during some periodof time, for instance, one to two seconds. Because user equipment maymake multiple access attempts, base station 902 may have the opportunityto recognize a bad estimate of S and instruct the sensor to adjust itsvalue of M. With a sufficiently low duty cycle on the scanning for S,the power consumption advantages of using a sensor-based wirelesscommunication network can be preserved. In this way, compressivesampling activities by sensor 910 may adaptively track the sparseness ofthe signals, which may affect it. Therefore, sensor 910 may minimize itspower consumption even while continuously performing compressivesampling.

At block 972, method 900 can use the sparseness S determined at block971 to retain indices of the largest S elements of the estimate of theinformation signal (“x”). At block 973, method 900 can use the S indicesdetermined at block 972 to set the largest S elements of the estimate ofthe information signal (“x”) to first value 974. At block 975, method900 can then set the remaining N−S elements of the estimate of theinformation signal (“x”) to second value 976. The output of quantizer953 can be a quantized estimate of the information signal (“x”),referred to as {circumflex over (x)}. First value 974 may be, forinstance, a logical one. Further, second value 976 may be, for instance,a logical zero.

FIG. 10 is chart 1000 illustrating an example of the type of sparserepresentation matrix and sensing matrix used in sensor-based wirelesscommunication system 100, 200, 300, 400, 600 and 800 using compressivesampling in accordance with various aspects set forth herein. In oneembodiment, a sensor-based wireless communication system usingcompressive sampling may use random matrices for the sparserepresentation matrix (“Ψ”) and the sensing matrix (“Φ”). The randommatrices are composed of, for instance, independently and identicallydistributed (“iid”) Gaussian values.

In another embodiment, a sensor-based wireless communication systemusing compressive sampling may use deterministic matrices for the sparserepresentation matrix (“Ψ”) and the sensing matrix (“Φ”). Thedeterministic matrices are composed of, for instance, an identity matrixfor the sparse representation matrix (“Ψ”) and a cosine matrix for thesensing matrix (“Φ”). A person of ordinary skill in the art wouldrecognize that many different types and combinations of matrices mightbe used for a sensor-based wireless communication system usingcompressive sampling.

FIG. 11 illustrates one embodiment of user equipment 1100, which can beused in sensor-based wireless communication system 100, 200, 300, 400,600 and 800 using compressive sampling in accordance with variousaspects set forth herein. In FIG. 11, user equipment 1100 can includemodulator 1140 for modulating an uplink message to form an informationsignal (“x”). Generator 1141 can receive the information signal (“x”)and can apply a sparse representation matrix (“Ψ”) 1143 to theinformation signal (“x”) to generate an uplink signal (“f”), which istransmitted by uplink transmitter 1142 using, for instance, antenna1364. User equipment 1100 can also include a downlink receiver 1148 fordownconverting a downlink signal received by antenna 1164. The receiveddownlink signal can then be processed by demodulator 1149 to generate adownlink message.

In this embodiment, user equipment 1100 can include oscillator 1162 forclocking user equipment 1100 and maintaining system timing, power supply1163 such as battery 1361 for powering user equipment 1100, input/outputdevices 1367 such as a keypad and display, memory 1360 coupled tocontroller 1147 for controlling the operation of user equipment 1100,other elements or combination of elements. A person of ordinary skill inthe art will recognize the typical elements found in a user equipment.

FIG. 12 illustrates one embodiment of a sensor 1200, which can be usedin sensor-based wireless communication system 100, 200, 300, 400, 600and 800 using compressive sampling in accordance with various aspectsset forth herein. In FIG. 12, sensor 1200 can include receiving element1230 for downconverting an uplink signal (“f”) received by, forinstance, antenna 1264. Compressive sampler 1231 can apply a sensingmatrix (“Φ”) 1233 to the uplink signal (“f”) to generate a sensed signal(“y”), which can be sent using sensor transmitter 1232.

In this embodiment, sensor 1200 can include oscillator 1262 for clockingsensor 1200 and maintaining system timing, power supply 1263 such asbattery 1261 for powering user equipment 1100, memory 1260 coupled tocontroller or state machine 1237 for controlling the operation of sensor1200, other elements or combination of elements. Controller 1237 may beimplemented in hardware, software, firmware or any combination thereof.Further, controller 1237 may include a microprocessor, digital signalprocessor, memory, state machine or any combination thereof.

FIG. 13 illustrates one embodiment of base station 1300, which can beused in sensor-based wireless communication system 100, 200, 300, 400,600 and 800 using compressive sampling in accordance with variousaspects set forth herein. In FIG. 13, in the uplink direction, basestation 1300 can include collector 1350 for collecting sensed signal(“y”). Detector 1351 can receive the collected sensed signal (“y”) andcan use a sensing matrix (“Φ”) 1233 and a sparse representation matrix(“Ψ”) 1143 to estimate and detect information signal (“x”) from thecollected sensed signal (“y”). Controller 1357 may evaluate the detectedinformation signal (“{circumflex over (x)}”) to determine the uplinkmessage. In the downlink direction, base station 1300 can include amodulator 1359 for modulating a downlink message and downlinktransmitter interface 1358 for sending the modulated downlink signals.

In this embodiment, base station 1300 can include oscillator 1362 forclocking base station 1300 and maintaining system timing, power supply1363 for powering base station 1300, memory 1360 coupled to controller1337 for controlling the operation of base station 1300, sensorcontroller 1355 for controlling a sensor, downlink transmittercontroller for controlling a downlink transmitter, other elements orcombination of elements.

In one embodiment, sensor-based wireless communication system 100, 200,300, 400, 600 and 800 may use a plurality of sensors 110 to 113, 210 to213, 310, 610, 710, 810, 1200 and 1310 to process uplink signal (“f”) toallow for the joint detection of a presence signal at base station 102,202, 302, 602, 702, 802 and 1302 by using antenna array signalprocessing techniques, MIMO signal processing techniques, beamformingtechniques, other techniques or combination of techniques. The use of aplurality of sensors 110 to 113, 210 to 213, 310, 610, 710, 810, 1200and 1310 may allow the value of M to be lower at each sensor 110 to 113,210 to 213, 310, 610, 710, 810, 1200 and 1310. Therefore, the powerconsumption of each sensor 110 to 113, 210 to 213, 310, 610, 710, 810,1200 and 1310 may be reduced by placing the plurality of sensors 110 to113, 210 to 213, 310, 610, 710, 810, 1200 and 1310, for instance, in amore dense deployment.

In another embodiment, sensor-based wireless communication system 100,200, 300, 400, 600 and 800 may deploy sensors 110 to 113, 210 to 213,310, 610, 710, 810, 1200 and 1310 to allow typically two sensors 110 to113, 210 to 213, 310, 610, 710, 810, 1200 and 1310 to receive uplinksignals (“f”) transmitted by user equipment 706. Such a deployment maybe in an indoor environment where sensors 110 to 113, 210 to 213, 310,610, 710, 810, 1200 and 1310 may be deployed by, for instance, a thirtymeters separation distance with a path loss exponent between two orthree. Sensors 110 to 113, 210 to 213, 310, 610, 710, 810, 1200 and 1310may each be deployed to cover a larger area; however, the path lossexponent may be smaller. For successful detection, the probability ofdetecting a single presence signal may be above ten percent.

In another embodiment, sensor-based wireless communication system 100,200, 300, 400, 600 and 800 may deploy sensor 110 to 113, 210 to 213,310, 610, 710, 810, 1200 and 1310 in macrocells to support, forinstance, vehicular communication, other communication or combination ofcommunication. Further, sensor 110 to 113, 210 to 213, 310, 610, 710,810, 1200 and 1310 may be deployed in microcells to support, forinstance, pedestrian communication, indoor communication, officecommunication, other communication or combination of communication.

In system 100, 200, 300, 400, 600 and 800, channel 620 and 820 may bestatic with channel gain (“a”) 621 and 821 and channel noise (“v”) 622and 821 may be additive white Gaussian noise (“AWGN”). Channel noise(“v”) 622 and 821 may include an additive signal, which may distort thereceiver's view of the information of interest. The source of thechannel noise (“v”) may be, for instance, thermal noise at a receiveantenna, co-channel interference, adjacent channel interference, othernoise sources or combination of noise sources. Further, sensor 110 to113, 210 to 213, 310, 610, 710, 810, 1200 and 1310; user equipment 106,206, 306, 606, 706, 806 and 1100; base station 102, 202, 302, 602, 702,802 and 1302; or any combination thereof may be sufficientlysynchronized in timing, frequency, phase, other conditions orcombination of conditions thereof. In addition, there may be only onesensor 110 to 113, 210 to 213, 310, 610, 710, 810, 1200 and 1310; oneuser equipment 106, 206, 306, 606, 706, 806 and 1100; one base station102, 202, 302, 602, 702, 802 and 1302; or any combination thereof.

The compressive sampling scheme may use a sparse representation matrix(“Ψ”) and a sensing matrix (“Φ”) that are, for instance, a random pair,a deterministic pair or any combination thereof. For these matrices,base station 102, 202, 302, 602, 702, 802 and 1302, sensor 110 to 113,210 to 213, 310, 610, 710, 810, 1200 and 1310, user equipment 106, 206,306, 606, 706, 806 and 1100, or any combination thereof may be providedwith, for instance, the sparse representation matrix (“Ψ”), the sensingmatrix (“Φ”) or both, information such as a seed value to generate thesparse representation matrix (“Ψ”), the sensing matrix (“Φ”) or both, orany combination thereof. Base station 102, 202, 302, 602, 702, 802 and1302 may know which sparse representation matrix (“Ψ”) and sensingmatrix (“Φ”) are being used. Base station 102, 202, 302, 602, 702, 802and 1302 may instruct sensor 110 to 113, 210 to 213, 310, 610, 710, 810,1200 and 1310 to use a specific set of M sensing waveforms (“φ_(j)”) ofsensing matrix (“Φ”). Further, base station 102, 202, 302, 602, 702, 802and 1302 may instruct user equipment 106, 206, 306, 606, 706, 806 and1100 and sensor 110 to 113, 210 to 213, 310, 610, 710, 810, 1200 and1310 that the uplink signal consists, for instance, of N intervals orchips.

The aforementioned random matrices, deterministic matrices or both maybe generated only once or may not change if generated again. Further,these matrices may be regenerated after some time, for instance, a fewseconds. Also, these matrices may be regenerated each time they are tobe used. In any case, the detector, which includes the solver, of basestation 102, 202, 302, 602, 702, 802 and 1302 may know the sparserepresentation matrix (“Ψ”) used by user equipment 706 as well as thesensing matrix (“Φ”) used by the sampler. A person of ordinary skill inthe art would recognize that this does not mean that the base stationmust provide the matrices. On the other hand, for example, userequipment 106, 206, 306, 606, 706, 806 and 1100 and base station 102,202, 302, 602, 702, 802 and 1302 may change the sparse representationmatrix (“Ψ”) according to, for instance, a pseudo-noise (“pn”) functionof the system time. Similarly, for example, sensor 110 to 113, 210 to213, 310, 610, 710, 810, 1200 and 1310 and base station 102, 202, 302,602, 702, 802 and 1302 may change the sensing matrix (“Φ”) according to,for instance, a pseudo-noise (“pn”) function of the system time.

FIG. 14 illustrates simulated results of one embodiment of detecting auser equipment in a sensor-based wireless communication system usingcompressive sampling in accordance with various aspects set forthherein, where the performance of system 800 was measured using N=10,M=5, S=1 or 2, and random matrices. The graphical illustration in itsentirety is referred to by 1400. The logarithmic magnitude of thesignal-to-noise (“SNR”) ratio is shown on abscissa 1401 and is plottedin the range from 0 decibels (“dB”) to 25 dB. The probability ofdetection (“Pr (detect)”) is shown on ordinate 1402 and is plotted inthe range from zero, corresponding to zero probability, to one,corresponding to one hundred percent probability. Graphs 1403, 1404 and1405 represent simulation results for system 800, where N is ten, M isfive, S is one or two and random iid Gaussian values are used topopulate the sparse representation matrix (“Ψ”) and the sensing matrix(“Φ”). Graph 1403 shows the probability of detecting one non-zero entryin a quantized estimate of the information signal (“x”), where S is one.Graph 1404 shows the probability of detecting one non-zero entry in aquantized estimate of the information signal (“x”), where S is two.Graph 1405 shows the probability of detecting two non-zero entries in aquantized estimate of the information signal (“x”), where S is two.

FIG. 15 illustrates simulated results of the performance of oneembodiment of a sensor-based wireless communication system usingcompressive sampling in accordance with various aspects set forthherein, where the performance of system 800 was measured using N=20,M=10, S=1 or 2, and random matrices. The graphical illustration in itsentirety is referred to by 1500. The logarithmic magnitude of the SNRratio is shown on abscissa 1501 and is plotted in the range from 0 dB to25 dB. The probability of detection (“Pr (detect)”) is shown on ordinate1502 and is plotted in the range from zero, corresponding to zeroprobability, to one, corresponding to one hundred percent probability.Graphs 1503, 1504, 1505, 1506 and 1507 represent simulation results forsystem 800, where N is twenty, M is ten, S is one or two and random iidGaussian values are used to populate the sparse representation matrix(“Ψ”) and the sensing matrix (“Φ”). Graph 1503 shows the probability ofdetecting one non-zero entry in a quantized estimate of the informationsignal (“x”), where S is one. Graph 1504 shows the probability ofcorrectly detecting two non-zero entries in a quantized estimate of theinformation signal (“x”), where S is two. Graph 1505 shows theprobability of correctly detecting no non-zero entries in a quantizedestimate of the information signal (“x”), where S is one. Graph 1506shows the probability of correctly detecting no non-zero entries in aquantized estimate of the information signal (“x”), where S is two.Graph 1507 shows the probability of correctly detecting one non-zeroentry in a quantized estimate of the information signal (“x”), where Sis two.

FIG. 16 illustrates simulated results of the performance of oneembodiment of a sensor-based wireless communication system usingcompressive sampling in accordance with various aspects set forthherein, where the performance of system 800 was measured using N=10,M=3, S=1, and deterministic or random matrices. The graphicalillustration in its entirety is referred to by 1600. The logarithmicmagnitude of the SNR ratio is shown on abscissa 1601 and is plotted inthe range from 0 dB to 25 dB. The probability of detection (“Pr(detect)”) is shown on ordinate 1602 and is plotted in the range fromzero, corresponding to zero probability, to one, corresponding to onehundred percent probability. Graphs 1603, 1604, 1605, 1606 and 1607represent simulation results for system 800, where N is twenty, M isten, S is one or two and deterministic values are used for the sparserepresentation matrix (“Ψ”) and the sensing matrix (“Φ”). Graph 1603shows the probability of correctly detecting one non-zero entry in aquantized estimate of the information signal (“x”), where S is one.Graph 1604 shows the probability of correctly detecting two non-zeroentries in a quantized estimate of the information signal (“x”), where Sis two. Graph 1605 shows the probability of correctly detecting nonon-zero entries in a quantized estimate of the information signal(“x”), where S is one. Graph 1606 shows the probability of correctlydetecting no non-zero entries in a quantized estimate of the informationsignal (“x”), where S is two. Graph 1607 shows the probability ofcorrectly detecting one non-zero entry in a quantized estimate of theinformation signal (“x”), where S is two.

FIG. 17 illustrates simulated results of the performance of oneembodiment of a sensor-based wireless communication system usingcompressive sampling in accordance with various aspects set forthherein, where the performance of system 800 was measured using N=10,M=3, S=1, and random or deterministic matrices. The graphicalillustration in its entirety is referred to by 1700. The logarithmicmagnitude of the SNR ratio is shown on abscissa 1701 and is plotted inthe range from 0 dB to 45 dB. The probability of detection (“Pr(detect)”) is shown on ordinate 1702 and is plotted in the range fromzero, corresponding to zero probability, to one, corresponding to onehundred percent probability. Graphs 1703, 1704, 1705 and 1706 representsimulation results for system 800, where N is ten, M is three and S isone. Graph 1703 shows the probability of correctly detecting onenon-zero entry in a quantized estimate of the information signal (“x”),where deterministic matrices are used. Graph 1704 shows the probabilityof correctly detecting one non-zero entry in a quantized estimate of theinformation signal (“x”), where iid Gaussian random matrices are used.Graph 1705 shows the probability of correctly detecting no non-zeroentries in a quantized estimate of the information signal (“x”), whereiid Gaussian random matrices are used. Graph 1706 shows the probabilityof correctly detecting no non-zero entries in a quantized estimate ofthe information signal (“x”), where deterministic matrices are used.

FIG. 18 illustrates simulated results of the performance of oneembodiment of a sensor-based wireless communication system usingcompressive sampling in accordance with various aspects set forthherein, where the performance of system 800 was measured using N=10,M=5, S=2, and random matrices. Further, the sparse representation matrix(“Ψ”) and the sensing matrix (“Φ”) were varied prior to eachtransmission of the information signal (“x”). The graphical illustrationin its entirety is referred to by 1800. The logarithmic magnitude of theSNR ratio is shown on abscissa 1801 and is plotted in the range from 0dB to 50 dB. The probability of detection (“Pr (detect)”) is shown onordinate 1802 and is plotted in the range from zero, corresponding tozero probability, to one, corresponding to one hundred percentprobability. Graphs 1803, 1804, 1805 and 1806 represent simulationresults for system 800, where N is ten, M is five, S is two, random iidGaussian matrices are used for the sparse representation matrix (“Ψ”)and the sensing matrix (“Φ”) and the random matrices are regeneratedprior to each transmission. Graph 1803 shows the probability ofdetecting two non-zero entries in a quantized estimate of theinformation signal (“x”). Graph 1804 shows the probability of detectingtwo non-zero entries in a quantized estimate of the information signal(“x”), where any two sensing waveforms (“φ_(j)”) of sensing matrix (“Φ”)are substantially incoherent. Graph 1805 shows the probability ofdetecting one non-zero entry in a quantized estimate of the informationsignal (“x”), where any two sensing waveforms (“φ_(j)”) of sensingmatrix (“Φ”) are substantially incoherent. Specifically, graph 1804 andgraph 1805 also represent the effect of rejecting any two sensingwaveforms (“φ_(j)”) of sensing matrix (“Φ”) having a correlationmagnitude greater than 0.1. Graph 1806 shows the probability ofdetecting one non-zero entry in a quantized estimate of the informationsignal (“x”).

FIG. 19 illustrates simulated results of the performance of oneembodiment of a sensor-based wireless communication system usingcompressive sampling in accordance with various aspects set forthherein, where the performance of system 800 was measured using N=10,M=3, S=1, random matrices, and various number of trials. Further, thesparse representation matrix (“Ψ”) and the sensing matrix (“Φ”) werevaried prior to each transmission of the information signal (“x”). Thegraphical illustration in its entirety is referred to by 1900. Thelogarithmic magnitude of the SNR ratio is shown on abscissa 1901 and isplotted in the range from 0 dB to 50 dB. The probability of detection(“Pr (detect)”) is shown on ordinate 1902 and is plotted in the rangefrom zero, corresponding to zero probability, to one, corresponding toone hundred percent probability. Graphs 1903, 1904, 1905, 1906 and 1907represent simulation results for system 800, where N is ten, M is three,S is one, random iid Gaussian matrices are used for the sparserepresentation matrix (“Ψ”) and the sensing matrix (“Φ”) and the randommatrices are regenerated prior to each transmission. Graph 1903 showsthe probability of detecting one non-zero entry in a quantized estimateof the information signal (“x”), where any two sensing waveforms(“φ_(j)”) of sensing matrix (“Φ”) are substantially incoherent and twohundred trials are performed. Specifically, graph 1903 also representsthe effect of rejecting any two sensing waveforms (“φ_(j)”) of sensingmatrix (“Φ”) having a correlation magnitude greater than 0.1. Graph 1904shows the probability of correctly detecting one non-zero entry in aquantized estimate of the information signal (“x”), where two hundredtrials are performed. Graph 1905 shows the probability of correctlydetecting one non-zero entry in a quantized estimate of the informationsignal (“x”), where four thousand trials are performed. Graph 1906 showsthe probability of correctly detecting one non-zero entry in a quantizedestimate of the information signal (“x”), where one thousand trials areperformed. Graph 1907 shows the probability of correctly detecting onenon-zero entry in a quantized estimate of the information signal (“x”),where two thousand trials are performed.

FIG. 20 is an example of deterministic matrices used in one embodimentof a sensor-based wireless communication system using compressivesampling in accordance with various aspects set forth herein. Theexample of the deterministic matrices is collectively referred to as2000. Matrices 2001 and 2002 are representative of the deterministicmatrices that can be used in systems 100, 200, 300, 400, 600 and 800,where N is ten and M is five. Matrix 2001 can represent the transform ofthe sensing matrix (“Φ”). Matrix 2002 can represent the sparserepresentation matrix (“Ψ”).

FIG. 21 is an example of random matrices used in one embodiment of asensor-based wireless communication system using compressive sampling inaccordance with various aspects set forth herein. The example of therandom matrices is collectively referred to as 2100. Matrices 2101 and2102 are representative of the random matrices that can be used insystems 100, 200, 300, 400, 600 and 800, where N is ten and M is five.Matrix 2101 can represent the transform of the sensing matrix (“Φ”).Matrix 2102 can represent the sparse representation matrix (“Ψ”).

A different way of sampling is shown in FIG. 22. This figure is based on[CW08]. The sampler in FIG. 22 is a set of sensing waveforms, Φ. Thesignal, x, can be recovered without error if f is sparse. An Ndimensional signal is S-sparse, if in the representation f=Ψx,x only hasS nonzero entries (see [CW08, page 23]). Representation parameters arethe parameters which characterize the variables in the expression f=Ψx.These parameters include the number of rows in Ψ, i.e. N, the values ofthe elements of Ψ, and the number of nonzero entries in x, i.e. S. Thesteps of sampling and recovery in FIG. 22 are replaced by a new pair ofoperations, sensing and solving.

Step 1. Sensing.

y_(k)=

f,φ_(k)

,kεJ such that J⊂{1, . . . , N},  (4)

Step 2. Solving.

min_({tilde over (x)}ε)

_(N) ∥{tilde over (x)}∥

₁ subject to y _(k)=

φ_(k) ,Ψ{tilde over (x)}

,∀kεJ,  (5)

Equations (1) and (2) are from [CW08, equations 4 and 5]. In Eq. (1),the brackets, < >, denote inner product, also called correlation. The l₁norm, indicated by ∥{tilde over (x)}∥₁₁, is the sum of the absolutevalues of the elements of its argument.

In order to use as few sensing waveforms as possible, the coherencebetween the vectors of the basis, Ψ and the vectors used for sensingtaken from Φ must be low [CW08, equations 3 and 6]. The coherence, μ isgiven by

μ(Φ,Ψ)=√{square root over (N)}max_(1≦k,j≦N)∥

φ_(k),ψ_(j)

∥_(l) ₁ ,  (6)

The Incoherent Sampling Method for designing a sampling system (comparewith [CW08]) is:

1. Model f and discover a Ψ in which f is S-sparse.

2. Choose a Φ which is incoherent with Ψ.

3. Randomly select M columns of Φ, where M>S.

4. Sample f using the selected φ vectors to produce y.

5. Pass Ψ, Φ and y to an l₁ minimizer, and recover x.

One method which can be applied for l₁ minimization is the simplexmethod [LY08].

An embodiment of the invention shown in FIG. 23 includes a low powerreceiver. The RF portions of the low power receiver can be implementedas taught in [ESY05, KJR+06]. The figure represents a multiple accesssystem 2300. The multiple Access Schemes that can be used in the system,include FDMA, TDMA, DS-CDMA, TD/CDMA using FDD and TDD modes [Cas04, pp.23-45, 109] and OFDM access scheme [AAN08]. The system includes a userequipment or UE 2206 and an infrastructure 2210. The UE 2206 includes amobile station, cellular-radio equipped laptop computer, and smartphone. The infrastructure 2210 includes the parts of the cellularsystem, which is not the UE, such as remote samplers 2212, base station2216, central brain, and DL tower 2222. The remote samplers 2212includes a device consisting of an antenna, a down-conversion RFsection, a correlating section, a controller or state machine forreceiving instructions over a backhaul, a memory for storing aconfiguration and optical transmitter to send the correlation results orvalue over a fiber (back-haul) to the base station 2216. Each basestation 2216 will be fed by more than one remote sampler 2212, ingeneral. Remote samplers 2212 may be deployed in a system using theCentral Brain concept, or in a system not using the Central Brainconcept.

Conversion includes representing an input waveform is some other formsuitable for transmission or computation. Examples are shifting thefrequency of a signal (down conversion), changing from analog to digitalform (A to D conversion).

The central brain is a high-powered infrastructure component which cancarry out computations at a very high speed with acceptable cost. Thecentral brain includes infrastructure components which can communicatewith the base stations quickly so that many physical layer computingactivities can be carried out at the Central Brain. Radio control viathe base station and the DL tower is not so slow as to be infeasible toovercome communications impairments associated with the rate of fadingof the channel. The Central Brain and the Base Station may physically bethe same computer or infrastructure component. The base stationtransmitter is located at the DL (downlink) Tower 2222 which includes aconventional cellular tower, cellular transmitters mounted on buildings,light poles or low power units in offices.

The downlink, DL 2220 is the flow of information-bearing RF energy fromthe infrastructure to the User Equipment or UE. This includes radiosignals transmitted by the DL tower 2222 and received by a UE 2206.

Fading includes descriptions of how a radio signal can be bounced offmany reflectors and the properties of the resulting sum of reflections.Please see [BB99, Ch. 13] for more information on fading.

Environmental parameters includes the range from the UE to the remotesampler, the range from the UE to the DL tower, the SNR at any remotesampler of interest and any co channel signal which is present and anyfading.

There are several kinds of access in cellular systems. Aloha randomaccess takes place when the UE wishes to reach the infrastructure, butthe infrastructure does not know the UE is there. Two-way data exchangetakes place after the UE has been given permission to use the system andUL and DL channels have been assigned. For more discussion of access,please see [Cas04, pg. 119].

“Channels” include permitted waveforms parameterized by time, frequency,code and/or space limitations. An example would by a particular TDMAslot in a particular cell sector in a GSM system. User data and/orsignaling information needed for maintaining the cellular connection aresent over channels.

The term “Base Station” is used generically to include description of anentity which receives the fiber-borne signals from remote samplers,hosts the l1 solver and Quantizer and operates intelligently (that is,runs computer software) to recognize the messages detected by theQuantizer to carry out protocol exchanges with UEs making use of the DL.It generates the overhead messages sent over the DL. It is functionallypart of the Central Brain concept created by RIM. A “Solver” includes adevice which uses the l1 distance measure. This distance is measured asthe sum of the absolute values of the differences in each dimension. Forexample, the distance between (1.0, 1.5, 0.75) and (0, 2.0, 0.5) is|1−0|+|1.5−2.0|+|0.75−0.5|=1.75. A “Quantizer” includes a device whichaccepts an estimate as input and produces one of a finite set ofinformation symbols or words as output.

The base station receiver, solver, quantizer, and a controller are atthe point called “base station” 2216 in the figure. The base station2216 and DL Tower 2222 could be co-located, and in any event they arecompletely connected for signaling purposes. Uplink 2224 is the flow ofinformation-bearing RF energy from the UE 2206 to the infrastructure2210. This includes radio signals transmitted by the UE 2206 andreceived by one or more remote samplers 2212.

Cellular systems provide multiple access to many mobile users for realtime two way communication. Examples of these systems are GSM, IS-95,UMTS, and UMTS-Wi-Fi [Cas04, pg. 559].

A mixed macro/micro cellular network includes large cells for vehiclesand small cells for pedestrians [Cas04, pg. 45]. For a generalperspective on cellular system design, the GSM or WCDMA systems aresuitable reference systems. That is, they exhibit arrangements of mobilestations (UEs), base stations, base station controllers and so on. Inthose systems various signaling regimes are used depending on the phaseof communication between the UE and the infrastructure such as randomaccess, paging, resource allocation (channel assignment), overheadsignaling (timing, pilot system id, channels allowed for access),handover messaging, training or pilot signals on the uplink and downlinkand steady state communication (voice or data, packet or circuit).

Feeding an unsampled analog signal to a base station via a fiber waspresented in [CG91]. In Chu, a kind of transducer is attached to anantenna and feeds a fiber. The transducer in [CG91] does not sample theRF signal, it simply converts it to optical energy using an analog lasertransmitter. Part of the novelty of this invention is the number andnature of values sent to the base station from a remote antenna and howthe number and nature is controlled.

FIG. 24 is often thought of in the context of lossless sampling. If thepower spectrum of a signal A(f) is zero for |f|>fmax, then the timedomain signal a(t) can be represented based on discrete samples taken atrate 2fmax [Pro83, page 71]. In this general scenario, the only thingthe sampler knows about A(f) is that it is zero above fmax.

For a radio system in which the sampler is locked to the chip rate, ingeneral, lossless sampling would consist of sampling once per chip. Foran N chip waveform, which includes a frame defined at N discrete,sequential points in time, this would mean N samples per chip-levelcodeword. The frame might be a frame ready for conversion to passbandfor transmission, or it might simply be a frame of boolean, real, orcomplex values inside of a computing device or memory. In one embodimentof this invention, N chip waveforms are sensed with M values, where M<N.“Frame” includes a collection of time samples captured in sequence. Itmay also describe a collection of boolean (or real or complex) valuesgenerated in sequence.

“Noise” includes an additive signal, which distorts the receiver's viewof the information it seeks. The source may be thermal noise at receiveantenna, or it may be co channel radio signals from undesired or otherdesired sources, or it may arise from other sources. The basic theory ofdetection of signals in noise is treated in [BB99, Ch. 2.6].

“Performance” includes how well a radio system is doing according to adesigner's intended operation. For instance, the designer may wish thatwhen a UE powers up and recognizes an overhead signal, it will send amessage alerting the base station. The performance of the base stationdetection of this signal includes the probability that the base stationwill recognize a single transmission of that message. The performancevaries depending on the system parameters and environmental factors.“System parameters” includes the length of message frames, the number ofsensing waveforms and the sparseness of the messages being sent.

The Uplink is the flow of information-bearing RF energy from the UE tothe infrastructure. This includes radio signals transmitted by the UEand received by one or more remote samplers. Incoherent samplingincludes a kind of compressive sampling which relies on sensingwaveforms (columns of Φ) which are unrelated to the basis, Ψ, in whichthe input signal is sparse. This report discloses simple sampling andlow rate data transmission to conserve battery power at the remotesampler, please see FIG. 25. Compressive sampling includes a techniquewhere a special property of the input signal, sparseness, is exploitedto reduce the number of values needed to reliably (in a statisticalsense) represent a signal without loss of desired information. Here aresome general points about the inventive architecture.

1. The overall cellular system continues to operate with fullperformance even if a sampler stops working.

2. The remote samplers are widely distributed with a spacing of 30 to300 m in building/city environments.

3. The base station is not limited in its computing power.

4. The cellular system downlink is provided by a conventional celltower, with no unusual RF power limitation.

5. UE battery is to be conserved, the target payload data transmissionpower level is 10 to 100 μWatts.

6. Any given remote sampler is connected to the base station by a fiberoptic. One alternative for selected sampler deployments would be coaxialcable.

7. If possible, the remote sampler should operate on battery power.Using line power (110 V, 60 Hz in US) is another possibility.

From the overall system characteristics, we infer the following traitsof a remote sampler.

1. The remote sampler is very inexpensive, almost disposable.

2. The remote sampler battery must last for 1-2 years.

3. The remote sampler power budget will not allow for execution ofreceiver detection/demodulation/decoding algorithms.

4. The remote sampler will have an RF down conversion chain and somescheme for sending digital samples to the base station.

5. The remote sampler will not have the computer intelligence torecognize when a UE is signaling.

6. The remote sampler can receive instructions from the base stationrelated to down conversion and sampling.

Examples of modulation schemes are QAM and PSK and differentialvarieties [Pro83, pp. 164, 188], coded modulation [BB99, Ch. 12].

From those traits, these Design Rules emerge:

Rule A: Push all optional computing tasks from the sampler to the basestation.

Rule B: Drive down the sampler transmission rate on the fiber to thelowest level harmonious with good system performance.

Rule C: In a tradeoff between overall system effort and sampler batterysaving, overpay in effort.

Rule D: Make the sampler robust to evolutionary physical layer changeswithout relying on a cpu download.

From the Design Rules, we arrived at the design sketched in FIGS. 23 and25. In this report, we have focused on the problem of alerting the basestation when a previously-unrecognized UE (User Equipment or mobilestation) is present. The situation is similar to one of the accessscenarios described in [LKL+08, “Case 1”], except that we have nottreated power control or interference here. There are well known methodsto control those issues. The sampler operates locked to a system clockprovided by the base station.

Please see FIG. 26 for an illustration of the messages being sent incellular system access event that this report is focused on. FIG. 26 isone example situation which illustrates the UE 2206 sending Presencesignals 2314. In the figure, the UE 2206 powers on, observes overheadsignals 2312, and begins to send Presence Alert signals 2314. The term“Presence Signal” includes any signal which is sent by the UE 2206 tothe base station which can be incoherently sampled by sense waveforms.“Sense waveforms” includes a column from the sensing matrix, Φ, which iscorrelated with a frame of the input to obtain a correlation value. Thecorrelation value is called y_(i) where i is the column of Φ used in thecorrelation. In general, the UE 2206 may use Presence Alert signals 2314whenever it determines, through overhead information 2312, that it isapproaching a cell which is not currently aware of the UE 2206. Theremote sampler 2212 sends sense measurements, y, continuously unlessM=0.

Sense parameters are the parameters which characterize the variables inthe expression. Overhead 2312 is sent continuously. The Presence Alertsignal 2314 is sent with the expectation that it will be acknowledged.The UE and base station exchange messages in this way: UL is UE 2206 toremote sampler 2212. The remote sampler 2212 continuously senses,without detecting, and sends sense measurements y to the base station2216 over a fiber optic. The DL is the base station tower 2222 to UE2206, for instance the message 2318 instructing UEs to use sparsity S₂when sending a Presence signal 2314. A sparse signal includes an N-chipwaveform which can be created by summing S columns from an N×N matrix.An important characteristic of this signal is the value of S,“sparsity”. For nontrivial signals, S ranges from 1 to N. An instruction2316 changing the value of M used by the remote sampler 2212 is shown.An indication is a way of messaging to a UE or instructing a remotesampler as the particular value of a particular variable to be used. Thefigure is not intended to show exactly how many messages are sent.

The UE also has access to the system clock via overhead transmissionsfrom the base station on the downlink (DL). The remote sampler observesa bandwidth of radio energy, B, centered at some frequency fc.Generally, it does not treat B as the only information it has, so itdoes provide samples at rate 2B over the fiber to the base station.Rather, the sampler obtains N samples of the N chip waveform, andcomputes M correlations. The resulting M values are sent over the fiberto the base station. If the sampler does not have chip timing lock, itcan acquire 2N samples at half-chip timing and compute 2M correlations.The reduction in samples sent to the base station is from 2N for aconventional approach to 2M.

The sampler is able to compute sensing measurements, y, by correlatingwith independently selected columns of the Φ matrix. Sensing parametersare the parameters which characterize the variables in the correlationof the received signal g with columns of the Φ matrix. These parametersinclude the number of elements in y, i.e. M, the values of the elementsof Φ, and the number of chip samples represented by g, i.e., N.Selection of the columns of the Φ matrix which are used is without anyknowledge of x except selection of the value of M itself relies on anestimate of S. So, which columns of Φ are used is independent of Ψ, butthe number of columns of Φ used is dependent on an estimate of aproperty of f. Or, the sparsity of f can be controlled by DLtransmissions as shown at time t17 in FIG. 26.

A necessary condition for successful detection of x at the base station,is that the value of M used by the remote sampler must be chosen greaterthan S. The lack of knowledge of S can be overcome by guessing at thebase station, and adjusting thereafter. For instance, M may start outwith a maximum value of N, and as the base station learns the activitylevel of the band B, M can be gear shifted to a lower, but stillsufficiently high, value. In this way, power consumption at the remotesampler, both in computing correlations, y, and in transmissions to thebase station on the fiber, can be kept low. The base station mightperiodically boost M (via instruction to the remote sampler) tothoroughly evaluate the sparsity of signals in the band B. The basestation can direct the sampler as to which columns it should use, or thesampler may select the columns according to a schedule, or the samplermay select the columns randomly and inform the base station as to itsselections.

Detection includes operating on an estimated value to obtain a nearestpoint in a constellation of finite size. A constellation includes a setof points. For example, if each point in the constellation is uniquelyassociated with a vector containing N entries, and each entry can onlytake on the values 0 or 1 (in general, the vector entries may bebooleans, or reals, or complex) then the constellation has 2N or fewerpoints in it.

The UE 2206, upon powering on, wishes to let the system know of itsexistence. To do this, the UE sends a Presence Alert signal 2314. ThePresence Alert signal is an informative signal constructed by selectingcolumns out of the Ψ matrix and summing them. The selection of columnscan be influenced by the base station overhead signal. For instance, thebase station may specify a subset of Ψ columns which are to be selectedfrom.

The base station can require, via a DL overhead message 2312, that a UEwhich has not yet been recognized, to transmit one particular column,say φ0. This would act as a pilot. The remote sampler 2212 wouldoperate, according to Incoherent Sampling, and send samples y to thebase station 2216. The base station 2216 would then process this signaland detect the presence of φ0, estimate the complex fading channel gain,{circumflex over (α)}, between the previously-unrecognized UE and theremote sampler, and then instruct any UEs which had been sending φ0 tocommence sending the last two bits of their ESN (Electronic SerialNumber, a globally unique mobile station identifier), for example.“Sampling” includes changing a signal from one which has values at everyinstant of time to a discrete sequence which corresponds to the input atdiscrete points in time (periodic or aperiodic).

If a collision occurs between transmissions from two different mobilestations the uplink (UL), standard Aloha random back-off techniques maybe used to separate subsequent UL attempts.

The remote sampler 2212 is unaware of this protocol progress, and simplykeeps sensing with columns from Φ and sending the samples y to the basestation 2216. The base station 2216 may instruct the remote sampler 2212to use a particular quantity, M, of sensing columns. This quantity mayvary as the base station anticipates more or less information flow fromthe UEs. If the base station anticipates that S, which has a maximum ofN, is increasing, it will instruct the remote sampler to increase M (themaximum value M can take on is N). For example, in FIG. 26, theRecognition Message can include a new value of S, S₃, to be used by theUE, and at the same time the base station can configure the remotesampler to use a higher value of M, called M₃ in the figure. In thefigure these events occur at times t₁₃, t₁₅ and t₁₆. At t₁₇ the basestation expects a message with sparsity S₃ and that that message hasprobably been sensed with an adequate value of M, in particular thevalue called here M₃. A sequence of events is illustrated, but thetiming is not meant to be precise. In the limit as M is increased, if Φis deterministic (for example, sinusoidal) and complex, when M takes onthe limiting value N, Φ in the remote sampler has become a DFT operation(Discrete Fourier Transform possibly implemented as an FFT). Continuingwith the scenario description, once the base station has a portion ofthe ESNs of all the UEs trying to access the system, the base stationcan tell a particular UE, with a particular partial ESN, to go ahead andtransmit its full ESN and request resources if it wishes. Or the basestation may assign resources, after determining that the UE is eligibleto be on this system.

The remote sampler/central brain system conducts information signalingin a noisy environment and with almost no intelligent activity at theremote sampler. The system has the benefit of feedback via aconventional DL. The link budget includes design of a radio system totake account of the RF energy source and all of the losses which areincurred before a receiver attempts to recover the signal. For moredetails, please see [Cas04, pp. 39-45, 381]. Our initial link budgetcalculations show that a UE may be able to operate at a transmissionpower of 10 to 100 μWatts at a range of 20 to 30 m if a reuse factor of3 can be achieved and a received SNR of 0 to 10 dB can be achieved.These figures are “order of” type quantities with no significant digits.For detection of the presence signal, usually more than one sampler canreceive noisy, different, versions of f and joint detection can be done.This will allow M to be lower at each sampler than if f is only visibleat one remote sampler. Thus, the battery drain at each sampler isreduced by deploying the samplers in a dense fashion. For brevity,sometimes the noisy version of f is referred to as g.

“Reuse” includes how many non-overlapping deployments are made of aradio bandwidth resource before the same pattern occurs againgeographically.

For a worst-case design, we assume the signal from the UE only impingeson one remote sampler. In general, for indoor transmission, we expecttwo remote samplers to be within a 30 m range with a path loss exponentbetween 2 and 3. The design is not limited to indoor transmission.Outdoors, the range will be larger, but the path loss exponent will tendto be smaller. For successful detection, the probability of detecting asingle transmission should be above 10% (presuming the error mechanismis noise-induced and therefore detection attempts will be independent).The remote sampler can be deployed in macro cells to support vehiculartraffic and microcells to support pedestrian or indoor-officecommunication traffic.

Coming to a concrete example, then, we have fashioned the followingscenario.

1. The channel is static (no fading).

2. The noise is AWGN.

3. The UE, remote sampler and base station are all locked to a clockwith no timing, frequency or phase errors of any kind. Impairments suchas these can be dealt with in standard ways [BB99, Ch. 5.8, Ch. 9].

4. There is one UE.

5. The Incoherent Sampling scheme uses a random pair (Ψ_(r), Φ_(r)) or adeterministic pair (Ψ_(d), Φ_(d)), in any case the solver knowseverything except the signals x, f and noise.

6. The base station has instructed the sampler to use a specific set ofM columns of Φ.

7. The base station has instructed the UE and the sampler thattransmission waveforms consist of N intervals or chips.

FIG. 27 is an illustration of one embodiment of the remotesampler/central brain cellular architecture in accordance with variousaspects set forth herein. The information is x 3240. f 3242 is S-sparse,and the base station has estimated S as discussed elsewhere. The inputto the remote sampler 3212 is a noisy version off, sometimes referred tohere as g 3244. The remote sampler 3212 computes M correlations of g3244 with preselected columns of Φ, producing the Mx1 vector y 3215(Equation 1). y 3215 is passed down a fiber optic to the base station3216.

“Estimation” is a statistical term which includes attempting to select anumber, {circumflex over (x)}, from an infinite set (such as the reals)which exhibits a minimum distance, in some sense, from the true value ofx. A frequently used measure of minimum distance is mean-squared error(MSE). Many estimators are designed to minimize MSE, i.e., Expectation{(x−{circumflex over (x)})²}. Statistical operations, such asExpectation, are covered in [Pro83, Ch. 1]. In practice, numbers outputfrom estimators are often represented with fixed-point values.

For reals, the correlation, or inner product, of g with φp is computedas y_(p)=Σ_(k=0) ^(N−1)φ_(p)(k)g(k), where the kth element of g isdenoted g(k).

For complex numbers the correlation would be y_(p)=Σ_(k=0)^(N−1)φ_(p)(k)g*(k), where g* denotes complex conjugation.

The l2 norm of a signal, g, is ∥g∥²=Σ_(k=0) ^(N−1)g(k)g*(k); theexpression for reals is the same, the complex conjugation has no effectin that case.

The base station 3216 produces first an estimate of x, called {tildeover (x)} 3246, and then a hard decision called {circumflex over (x)}3248. The estimate 3246 is produced by forming a linear program and thensolving it using the simplex algorithm. The algorithm explores theboundaries of a feasible region for realizations of the Nx1 vector x*which produce vectors y*. The search does not rely on sparsity. The l1minimization works because the signal is sparse, but the minimizer actswithout any attempt to exploit sparsity.

Hence, the N entries in x* are generally all nonzero. That x* whichproduces a y* which satisfies y*=y and has the minimum sum of absolutevalues is selected as {tilde over (x)} (Equation 5). {tilde over (x)} isgenerally not equal to x, so a hard decision is made to find the nearestvector {circumflex over (x)} to {tilde over (x)} consisting of S onesand N−S zeros.

Linear programs include a set of equations and possibly inequalities.The variables only appear in linear form. For example, if x1 and x2 arevariables, variables of the form x₁ ² do not appear.

The probability that this quantization identifies one or more correctnonzero entries in x is what the simulation is designed to determine.There are many definitions of “nearest”. We determine {circumflex over(x)} as follows. The quantizer 3230 first arithmetically-orders theelements of {tilde over (x)} and retain the indices of the first Selements (e.g., +1.5 is greater than −2.1). Secondly, the quantizer setsall the entries of {circumflex over (x)} to logical zero. Thirdly, thequantizer sets to logical one those elements of {circumflex over (x)}with indices equal to the retained indices. The result is the output ofthe quantizer.

The Quantizer 3230 obtains S from a variety of ways. Examples would bean all-knowing genie (for limiting performance determination) or thatthe base station has fixed the value of S to be used by the mobilestation, using the DL or that the base station periodically “scans” forS by trying different values (via instruction to the remote sampler) anddetermining the sparseness of f during some macro period of time, e.g.,1-2 seconds. Because UEs will make multiple attempts, the base stationhas opportunity to recognize a miss-estimate of S and instruct theremote sampler to reduce or increase the value it is using for S. With asufficiently low duty cycle on the scanning for S, the power-savingaspect of the sensing technique will be preserved. In this way, theremote sampler's sensing activities track the sparsity of the signalswhich impinge on it. Thus, the remote sampler is always sampling, ingeneral, but only with a battery drain sufficient for the system tooperate, and not much more battery drain than that. In particular, theremote sampler is not sampling at the full Nyquist rate for largeperiods when there is no UE present at all.

The y* is notation from [CW08, page 24]. The {circumflex over (x)} isnot notation from [CW08], because that reference does not treat signalscorrupted by noise. The {tilde over (x)} and {circumflex over (x)}notations for estimates and detected outputs are commonly used in theindustry, and can be seen, for example in [Pro83, page 364, FIG. 6.4.4“Adaptive zero-forcing equalizer”].

FIG. 27 shows the functional pieces and signals in the computersimulation. The nature of the matrices used is specified in Table 1. Thecolumns were normalized to unit length. Please see examples of thesematrices in FIGS. 20 and 21.

TABLE 1 Nature of the Matrices Nature Ψ_(ij) Φ_(ij) Random iid Gaussianiid Gaussian Deterministic 1 if i = j, else 0$\cos ( \frac{\pi \; {ij}}{N} )$

The deterministic matrices are generated only once, and would not changeif generated again. The random matrices might be generated only once, orthe random matrices may be regenerated after some time, such as a fewseconds. Also the random matrices may be regenerated each time they areto be used. In any case, the solver 3228 must know what Ψ matrix the UE3206 uses at any time and what Φ matrix the sampler 3212 uses. This doesnot mean the solver 3228 must dictate what matrices are used. If the UEis changing Ψ according to a pseudo-random (“pn”) function of the systemtime (time obtained via the DL overhead), then the solver 3228 can usethe same pn function generator to find out what Ψ was. Unless statedotherwise, the probabilities given in this report are for the case wherethe random matrices were generated once and fixed for all SNRs andtrials at those SNRs.

The simulation has been restricted to real numbers to ease development,but there is nothing in the schemes presented here that limits theirapplication to real numbers. The same building block techniques such ascorrelation and linear programming can be applied to systems typicallymodeled with complex numbers. This is true since any complex number a+jbcan be written as an all real 2×2 matrix with the first row being [a-b]and the second row being [b a].

This may be done at the scalar or the matrix level. Therefore anycomplex set of equations can be recast as an all-real set.

TABLE 2 Detector Performance with M = 5, N = 10. SNR(dB) S Pr{TotalMiss} Pr{j = 1 hit} Pr{j = 2 hit} 0 1 0.67 0.32 n/a 10 1 0.29 0.71 n/a20 1 0.12 0.87 n/a 0 2 0.44 0.46 0.09 10 2 0.22 0.47 0.30 20 2 0.16 0.280.55 AWGN. Ψ and Φ with iid Gaussian entries. See FIG. 27.

In these simulations, the performance we are looking for is anythingexceeding about 10%. A high number of trials is not needed as the onlyrandom events are the noise, the signal and the matrix generation. Thedata points were gathered using 100 or 200 trials per point in mostcases. In about 0.5% of the trials, our l1 solver implementationattempted to continue the optimization of {tilde over (x)} when itshould have exited with the existing solution. These few trials weretossed out. Even if included either as successes or failures, the effecton the results would be imperceptible, since we are looking for anyperformance greater than 10%.

The data from Table 3 is plotted in FIG. 14. S is the number of nonzeroentries in x and is called “pulses” in FIG. 14. The event “j=1 hit”means that the detector detected exactly one nonzero entry in xcorrectly. In the case that S=1, that is the best the detector can do.The event “j=2 hit” means that the detector detected exactly two nonzeroentries in x correctly.

I also did a simulation with M=3, N=10 and S=1 (please see FIG. 17discussed below).

TABLE 3 Detector Performance with M = 5, N = 10. SNR(dB) S Pr{TotalMiss} Pr{j = 1 hit} Pr{j = 2 hit} 0 1 0.64 0.36 n/a 10 1 0.13 0.87 n/a20 1 0.03 0.97 n/a 0 2 0.42 0.49 0.09 10 2 0.13 0.40 0.47 20 2 0.07 0.190.74 AWGN. Ψ and Φ with deterministic entries.

FIGS. 15, 16 and 17 give detection performance for various combinationsof M, N, S, SNR and nature of the matrices. In each of these plots j isthe number of nonzero entries in x correctly determined by thecombination of the l1 minimizer and the Quantizer (FIG. 25).

For system design, the important probability is the probability that thedetector gets the message completely right in one observation. Thesystem is assumed to use multiple transmissions, each of which will beindependent as to uncontrolled effects like noise. In that case, theprobability of detecting the Presence signal in C transmissions or lessis 1−Pr (Miss)C. A Miss can be defined either as the event j=0 or theevent j<S. When S=1 and with random matrices, the event j=S occurs withprobability greater than 10% at SNR below 0 dB, and at S=2 at SNR ofabout 3 dB. The 90% points are at about 12 and 17 dB respectively asseen in FIG. 15. The performance is better for deterministic matricesand S=1 as seen in FIG. 16.

In order to see how the detector would work when the sparsity condition(M>>S not true) was weak, we generated the data shown in FIG. 17 usingS=1 and M=3. Both the random and deterministic configurations are ableto detect at low SNR, but the random configuration saturates near 70%rather than reaching the 90% point. The performance for the randomconfiguration is a bit worse than that for M=5, N=10(e.g. Pr{detection}=0.55 at SNR=10 dB, while with M=5 this probability is 0.71).At high SNR, the probability approaches 1 for the deterministic case,FIG. 17.

Thus, we see that with increasing M and SNR, we approach Candesnoise-free result that 100% reliable exact recovery is reached. However,for low M and a noisy signal, sometimes the solver produces {tilde over(x)} is not equal to x. An important qualitative characteristic is thatthe degradation is gradual for the deterministic configuration. Athreshold effect in noise may exist with the random configuration unlessM>>S. In FIG. 17, M=3S, while in all of the other figures M≧5S for S=1.

An unusual characteristic of the Incoherent Sampling Method is theincoherence. Most detectors seek to try many candidate waveforms to seewhich one matches the received waveform and then use some kind of“choose largest” function to determine the identity, or index, of thetransmitted waveform. A local replica is a waveform which has the sameidentity as a transmitted waveform. In Incoherent Sampling, the onlyrequirement is that Ψ and Φ be weakly related at most. This means that agreat variety of sense matrices (Φs) could be used for any Ψ. For therandom case, we explored the effect of changing both matrices everytransmission. Results for this are shown in FIGS. 18 and 19. From thiswe noticed some variation in performance, even at high SNR. We confirmeda conjecture that this is due to the generation of “bad” matrices withpoor autocorrelation properties. High correlation within either matrixwould weaken the estimation ability, since for Ψ it would reduce thesupport for distinguishing the values of x on any two correlatedcolumns, and for Φ it would reduce the solver's ability to distinguishbetween candidate contributions from two correlated columns of Φ. Tolocalize the mechanism of these variations at high SNR, we rejected Φmatrices where any two columns had a correlation magnitude greater thana threshold. In the plots the threshold is 0.1. Studies were done withother thresholds. A threshold of 0.4 has almost no effect. What we havelearned from this is that, yes, there are wide variations in the effectof the actual Φ matrix on the performance. Another way to put this, isthat there are “bad” Φ matrices that we do not want to sense with. Theperformance is a random variable with respect to the distribution ofmatrices. This means that a probability of outage can be defined. Inparticular, the probability of outage is the probability that theprobability of detection will fall below a probability threshold. Forexample, the system can be designed so that not only the averageprobability of detection is greater than 40%, but the probability thatthe probability of detection will be less than 10% is less than 1%. Wecan reduce the number of “bad” matrices in order to reduce theprobability of outage. One way to do this is to constrain correlation inthe Φ matrices. Constraining the Ψ matrices will also be beneficial,especially as S increases.

To provide robust high bandwidth real time service and high user densityby radio, we have created an architecture based on dispersed antennasand centralized processing of radio signals. We call the system RemoteConversion or Remote Sampling. The mobile stations are simple low powerdevices, the infrastructure core is super-computer-like, and the BaseStations are linked to mobile stations by a redundant sea of cheap radiosensors. FIG. 28 is a diagram of the cellular network that we areproposing here. It shows a series of simple sensors 2712 deployed inlarge numbers such that generally more than one is within the range ofthe mobile subscriber (MS) device 2206. These sensors may also bereferred to as remote samplers or remote conversion devices in thisproject. The sensors could be separated in the range of ten meters to afew hundreds of meters. There is a deployment tradeoff between the powerrequired for the sensors, the ease of deploying the sensors and theamount of capacity needed in the system. The UE may use frequency bandsmuch higher than typical in cellular telephony.

The sensors are provided a fiber-optic back haul 2714 to a central basestation 2716. The backhaul could also be provided by another medium suchas coaxial cable. There may be several base stations in a deploymentwhere they communicate and pass information. The sensors have one ormore antennas attached to an RF front end and base-band processing thatis designed to be inexpensive. The sensors with one antenna can be usedas an array and can be made into MIMO air interfaces.

Beam-formed air interfaces allow the MS to transmit at a low power. Theupper layer protocol used between the MS and the Base Station could beone from a standardized cellular network (e.g. LTE). Upper LayerProtocols that specialize in low power and short range (e.g. Bluetooth)are alternative models for communications between the MS and BaseStation. The stack at the sensor will include only a fraction of layerone (physical). This is to reduce cost and battery power consumption.Possibly the sensors will be powered by AC (110 V power line in US). Lowround-trip time hybrid-ARQ retransmission techniques to handle real-timeapplications can be used; the Layer 2 element handling ARQ will not bein the sensor but rather in the BS or Central Brain. Areas of InnovationA completely new topology is given here in which the sensors compress ahigh bandwidth mobile signal received at short range and theinfrastructure makes physical layer calculations at high speed.

1. Instructions, communication protocols and hardware interfaces betweenthe base station and the sensors

a. remote conversion instructions

b. oscillator retuning instructions

c. beam steering (phase sampling) instructions

2. Communication protocols and hardware interfaces between the MS andthe BS or Central Brain

a. a high bandwidth MAC hybrid-ARQ link between an MS and the BS whichcan support real-time services.

3. Communication protocols and processing techniques between the MS andthe central processor/Central Brain

a. presence-signaling codes which work without active cooperation fromthe sensors

b. space time codes for this new topology and mixture of channelknowledge

c. fountain codes for mobile station registration and real timetransmission

d. large array signal processing techniques

e. signal processing techniques taking advantage of the higher frequencytransmission bands

4. The Base Stations support activities which include the following:

a. transmission of system overhead information

b. detection of the presence of mobile stations with range of one ormore sensors

c. two-way real-time communication between the base stations and mobilestation.

This memo addresses the sensor or sampler to be used in a cellulartelephony architecture. These sensors are cheaper than Base Stations andsample RF signals of high bandwidth, for example bandwidth B. Thecompressed signals are sent over fiber to the base station. The sensorsoften do not perform Nyquist sampling. This is done for several reasons.One is that sampling at high rates consumes much energy. We aim toprovide low-power sensor technology. Redundancy is expected to bedesigned into the system so that loss of single sensors can be easilyovercome. For many important signals, low-error reconstruction of thatsignal which is present can be done at the base station. A sensor may beequipped with a direct sequence de-spreader, or an FFT device. Thesensors do not make demodulation decisions. The direct sequence codeused in the de-spreader, or the sub-chip timing of the de-spreader orthe number of bins used in the FFT, or the spectral band the FFT is tobe applied to by the sensor are things which the Base Station tells thesensor through an instruction. In one embodiment, these instructionscome at 1 ms intervals and the sensor adjusts its sampling or conversionwithin less than 0.1 ms of receiving the instruction. For purposes ofstructure, we assume that the mobile station transmits and receivesinformation packets or frames of du-ration 1 to 5 ms. The format may becircuit-like or non-circuit-like. The system overhead information mayinclude guiding and synchronizing information which cause the mobilestations to practice and copy good cooperative behavior according togame theory. There may also be important information provided that theMS needs to know about a possible wireless WAN. By keeping allcommunications within this sub-communication network and not having tomonitor external networks, battery power can be saved. The mobilestations transmit their messages at low power. The sensors sample thewireless channel. The sensors in this proposal compress the samples. Thecompressed samples in the present proposal are sent over a fiber channelto the base station. The base station is responsible for many layer 1activities (demodulation, decoding), layer 2 activities (packetnumbering, ARQ), and signaling activities (registration, channelassignment, handoff). The computational power of the base station ishigh. The base station may use this computing power to solve equationsystems in real time that would have only been simulated offline inprior systems. The base station can use knowledge of the channel (mobilestation antenna correlation matrix, number of sensors in view of themobile station) to determine link adaptation strategies on a 1 msinterval. These strategies will include operating at the optimum spacetime multiplexing gain/diversity gain trade-off point. Also multiplebase stations can be in almost instantaneous communication with eachother, and optimally design transmit waveforms which will sum to yield adistortion-free waveform (dirty paper coding) at the simple mobilestation. Other base stations which receive extraneous uplink energy fromthe mobile station occasionally supply an otherwise-erased 1 ms frameinterval to the anchoring base station. FIG. 29 shows another schematicof the proposed system. The sensors 2712 in this proposal are onlyresponsible for sub-layer 1 activities, i.e., compression at the samplelevel. The Base Station 2716 in this proposal may send instructions tothe sensors, such as compress using multiple access code 16 (this mightbe a DS code, or OFDM code). The Base Station may send an instructionsuch as perform 2× sampling with phase theta. In other words, the sensoris a remote pulling away from an A/D path from a conventional basestation, like pulling a corner of taffy and creating a thin connectingstrand. The taffy strand is a metaphor for the fiber channel from asensor to the base station. The base station uses very high availablecomputing power to detect the presence of MS signals in the compresseddata. The base station in this proposal then responds to the detected MSby instructing the sensor to use sampling and compressing techniqueswhich will capture well the MS signal (timing, frequency, codingparticulars which render the compressed data full of the MS signal, eventhough the sensor is unaware of the utility of the instructions). The MSin this proposal may transmit with a fountain code, at least for callestablishment. For very high bandwidth, low power links, the mobilestation may transmit real time voice using a fountain code. The packettransmission rate should be with period on the order of 1 to 5 ms. Thesensor is primarily not a decision-making device; it is not locallyadaptive; sensor control is from the Base Station. The sensors aredeployed densely in space, that is, at least one every 100 m×100 m andpossibly one every 10 m×10 m. The sensors may or may not support a DLtransmission. The DL might be carried from a traditional base stationtower with sectorization. The density of such towers would be at leastone every 1000 m×1000 m (building deployment) and possibly one every 300m×300 m (street light deployment).

An example of a low cost radio is given in Kaukovuori [KJR+06], anotheris given in Enz [ESY05].

Using fiber to connect a remote antenna to a base station was proposedand tested by Chu [CG91].

Current Intel processors like the QX9775 execute at over 1 GHz clockspeed, at over 1 GHz bus speed and with over 1 MB cache. According toMoore's law, transistor densities will reach 8× their current value by2015. Based on the typical clock-rate-times gate-count reasoning, we canexpect roughly 10× the processing power will be available in singleprocessors in 2015. Thus, in 1 ms, 10 million CISC instructions can beexecuted. One microprocessor will direct the physical layer adaptationof 10 sensors in real time. http://compare.intel.com/pcc/

The limits on the MIMO multiplexing/diversity tradeoff were derived byZheng and Tse, 2L. Zheng and D. Tse, “Diversity and Multiplexing: AFundamental Tradeoff in Multiple-Antenna Channels, IEEE Transactions onInfo. Theory, May 2003, pp. 1073-1096”.

The present-day conception of dirty paper coding is discussed in, forexample, Ng, “C. Ng, and A. Goldsmith, Transmitter Cooperation in Ad-HocWireless Networks: Does Dirty-Paper Coding Beat Relaying?, IEEE ITW2004, pp. 277-282.”

Teaching selfish users to cooperate is discussed, for example, in Hales,“D. Hales, From Selfish Nodes to Cooperative Networks EmergentLink-based incentives in Peer-to-Peer Networks, IEEE Peer-to-PeerComputing, 2004”.

The concept of multiple nodes receiving cleverly-redundant transmissionis discussed in Kokalj-Filipovic, “A. Kokalj-Filipovic, P. Spasojevic,R. Yates and E. Soljanin, Decentralized Fountain Codes for Minimum-DelayData Collection, CISS 2008, pp. 545-550”.

From these tables and figures, we conclude that, yes, it has beenpossible to design a Presence signal and detect at the remote samplerwhile satisfying qualitative design rules. In particular, twocombinations Ψ and Φ have been shown to make detection of the Presencesignal possible with very little signal processing, and nodecision-making, at the remote sampler. Recall, the Presence signal is asum of columns from the Ψ matrix. The probability of detecting thePresence signal with S=1 or S=2 nonzero entries in x is sufficientlyhigh for SNRs in the range of 0 to 10 dB. This is achieved under theconstraint that the remote sampler transmits to the base station fewersamples than would be required for conventional conversion of theobserved signal when the conventional assumption has been made that thesignal fully exercises an N-dimensional basis. This gain has beenbrought about by purposefully designing the transmitted signal to besparse, the remote sampler to be simple, and the base station to beintelligent and equipped with a separately designed (non-co-located withthe remote samplers) downlink connection to mobile stations.

REFERENCES

-   [AAN08] K. Adachi, F. Adachi, and M. Nakagawa. Cellular mimo channel    capacities of mc-cdma and ofdm. IEEE, 2008.-   [BB99] S. Benedetto and E. Biglieri. Principles of Digital    Trans-mission With Wireless Applications. Kluwer, N.Y., 1999.-   [Cas04] J. P. Castro. All IP in 3G CDMA Networks. John Wiley & Sons,    Ltd., Chichester, England, 2004.-   [CG91] T. S. Chu and M. J. Gans. Fiber optic microcellular radio.    IEEE, pages 339-344, 1991.-   [CR02] S. Cotter and B. Rao. Sparse channel estimation via matching    pursuit with application to equalization. IEEE Trans. on    Communications, pages 374-377, March 2002.-   [CW08] E. Candes and M. Wakin. An introduction to compressive    sampling. IEEE Signal Proc. Mag., pages 21-30, March 2008.-   [ESY05] C. Enz, N. Scolari, and U. Yodprasit. Ultra low-power radio    design for wireless sensor networks. IEEE Intl. Workshop on RF    Integration Tech., pages 1-17, December 2005.-   [JR08] Y. Jin and B. Rao. Performance limits of matching pursuit    algorithms. IEEE Intl. Sym. Info. Theory, pages 2444-2448, July    2008.-   [KJR+06] J. Kaukovuori, J. A. M. Jarvinen, J. Ryynanen, J.    Jussila, K. Kivekas, and K. A. I. Halonen. Direct-conversion    re-ceiver for ubiquitous communications. IEEE, pages 103-106, 2006.-   [LKL+08] M. Lee, G. Ko, S. Lim, M. Song, and C. Kim. Dynamic    spectrum access techniques: Tpc-resilient initial access in open    spectrum bands. Intl. Conf. on Cognitive Radio Or-iented Wireless    Networks and Comm., pages 1-6, May 2008.-   [LY08] D. Luenberger and Y. Ye. Linear and Nonlinear Programming.    Springer, third edition, 2008.-   [Pro83] John G. Proakis. Digital Communications. McGraw-Hill, New    York, N.Y., first edition, 1983.-   [TGS05] J. A. Tropp, A. C. Gilbert, and M. J. Strauss. Simultaneous    sparse approximation via greedy pursuit. IEEE ICASSP, pages    V721-V724, 2005.

Having shown and described exemplary embodiments, further adaptations ofthe methods, devices and systems described herein may be accomplished byappropriate modifications by one of ordinary skill in the art withoutdeparting from the scope of the present disclosure. Several of suchpotential modifications have been mentioned, and others will be apparentto those skilled in the art. For instance, the exemplars, embodiments,and the like discussed above are illustrative and are not necessarilyrequired. Accordingly, the scope of the present disclosure should beconsidered in terms of the following claims and is understood not to belimited to the details of structure, operation and function shown anddescribed in the specification and drawings.

As set forth above, the described disclosure includes the aspects setforth below.

1. A method for sampling signals, the method comprising: receiving, overa wireless channel, a user equipment transmission based on an S-sparsecombination of a set of vectors; down converting and discretizing thereceived transmission to create a discretized signal; correlating thediscretized signal with a set of sense waveforms to create a set ofsamples, wherein a total number of samples in the set is equal to atotal number of sense waveforms in the set, wherein the set of sensewaveforms does not match the set of vectors, and wherein the totalnumber of sense waveforms in the set of sense waveforms is fewer than atotal number of vectors in the set of vectors; and transmitting at leastone sample of the set of samples to a remote central processor.
 2. Themethod of claim 1 wherein the set of vectors comprises at least one setselected from the list consisting of: a row of a basis matrix and acolumn of a basis matrix.
 3. The method of claim 1 further comprising:selecting a new set of sense waveforms responsive to receiving aninstruction from the remote central processor.
 4. The method of claim 1further comprising: adjusting a timing reference responsive to receivingan instruction from the remote central processor.
 5. The method of claim1 further comprising: changing the number of sense waveforms responsiveto receiving an instruction from the remote central processor.
 6. Themethod of claim 1, wherein the set of vectors and the set of sensewaveforms have a coherence value less than or equal to 0.45 multipliedby a square root of a dimension of a vector in the set of vectors.
 7. Amethod of wireless communication, the method comprising: receiving, at auser equipment, over a wireless channel, an indication of a first set ofrepresentation parameters; transmitting a first signal, wherein thefirst signal is based at least in part on the first set ofrepresentation parameters; receiving an indication of a second set ofrepresentation parameters; and transmitting a multiple access message,wherein the multiple access message is based at least in part on thesecond set of representation parameters.
 8. The method of claim 7wherein the multiple access message comprises at least a portion of aunique identification number for the user equipment.
 9. A method ofcommunication, the method comprising: receiving, at a central processor,a set of samples; forming a linear program with L1 minimization usingthe set of samples, a basis matrix and a set of sense waveforms; solvingthe linear program to produce an estimated set of data; and quantizingthe estimated set of data to produce a set of information symbols. 10.The method of claim 9 further comprising: selecting a first subset ofthe estimated set of data, wherein a total number of elements in thefirst subset is a representation parameter, and wherein all elements ofthe first subset are arithmetically larger than remaining elements ofthe estimated set of data; and identifying indices of elements of thefirst subset.
 11. The method of claim 10, wherein the set of informationsymbols form a binary vector having a length equal to a length of theestimated set of data, and consisting of a logical 1 at each positioncorresponding to one of the identified indices, and a logical 0 atremaining positions.
 12. The method of claim 10 further comprising:instructing a user equipment to use the representation parameter.
 13. Amethod of wireless communication, the method comprising: transmitting,to a user equipment, over a wireless channel, an instruction indicatinga first set of representation parameters; and transmitting, to a remotesampler, an instruction indicating a set of sensing parameters.
 14. Themethod of claim 13 further comprising: selecting the set of sensewaveforms based on the first set of representation parameters.
 15. Themethod of claim 13 further comprising: transmitting, to the userequipment, a set of system parameters.
 16. The method of claim 15wherein the set of system parameters comprises at least one selectedfrom the list consisting of: a system timing, a frame timing, anindication of a basis matrix, and a system clock.
 17. The method ofclaim 13 further comprising: receiving, from the remote sampler, a setof samples; and processing the received set of samples to produce a setof information symbols.
 18. The method of claim 17 further comprising:detecting a multiple access signal from the received set of samples. 19.The method of claim 18 further comprising: transmitting, to the userequipment, over a wireless channel, an instruction indicating a secondset of representation parameters, subsequent to detecting the multipleaccess message.